Equations of linear graphs — Paper 1 · IGCSE Mathematics 0580

12 For y Examiner's Use NOT TO 3 SCALE l x 0 1 A straight line, l, crosses the x-axis at (1, 0) and the y-axis at (0, 3). (a) Find the gradient of the line l. Answer(a) [1] (b) Write down the equation of the line l, in the form y = mx + c. Answer(b) y = [2]

3 marks

Mark scheme: 12 (a) −3 1 B1 for their (a)x or +3 as intercept seen (b) (y =) −3x + 3 2ft in the equation. Not y = 3 Final answer

This question in 0580/11 Oct/Nov 2007

12 The line with equation y = 2x − k passes through the point (4 , 0). Work out the value of k. Answer k = [2]

2 marks

Mark scheme: 12 (k=) 8 2 M1 for 0 = 2 × 4 − k or better

This question in 0580/11 Oct/Nov 2008

4 Write down the equation of the line, parallel to y = 4x + 1 , which passes through the point (0, −3). Answer [2]

2 marks

Mark scheme: 4 y = 4x – 3 oe 2 W1 for y = 4x + j, or y = kx − 3 If zero, SC1 for 4x – 3 k ≠ 0

This question in 0580/11 May/June 2010

6 Write down the equation of the line, parallel to y = 3x + 5 , which passes through the point (0, −2). Answer [2]

2 marks

Mark scheme: 6 y = 3x – 2 oe final answer 2 W1 for 3x + j, j ≠ 5 or W1 for kx − 2, k ≠ 0 11 3 × 8 5 × 1 5 24

This question in 0580/13 May/June 2010

19 For y Examiner's Use 2 x 0 6 The diagram shows a straight line passing through the points (0, 2) and (6, 0). Find the equation of this line in the form y = mx + c. Answer y = [3]

3 marks

Mark scheme: 1 1 19 (y =) −3 x + 2 cao 3 B1 for gradient of ± 3 oe (Allow ±0.33 or better) B1 ind for mx + 2 where m ≠ 0.

This question in 0580/13 Oct/Nov 2010

17 For y Examiner's B Use 6 5 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 A –3 –4 –5 –6 The diagram shows two straight lines, A and B, drawn on a grid. (a) Write down the equation of line A. Answer(a) [1] (b) The equation of line B is y = 3x – 1 . (i) Draw a line parallel to line B that passes through the point (0, 2). [1] (ii) Write down the equation of your line in the form y = mx + c. Answer(b)(ii) y = [2]

4 marks

Mark scheme: 17 (a) y = −2 or y + 2 = 0 1 (b) (i) Ruled line parallel to B through 1 Must at least go through (−1, –1) (0, 2) (ii) (y =) 3x + 2 cao final answer 2 B1 3x + j j ≠ –1 or 2 or kx + 2 k ≠ 3 SC1 for 3x + 2 then spoiled by the final answer

This question in 0580/12 Oct/Nov 2011

18 For y L Examiner's Use (4, 10) NOT TO SCALE x 0 –2 Line L passes through the point (4, 10). (a) Find the gradient of line L. Answer(a) [2] (b) Write down the equation of line L, in the form y = mx + c. Answer(b) y = [1] (c) Line P passes through the point (0, 0). Line P is parallel to line L. Write down the equation of line P. Answer(c) y = [1]

4 marks

Mark scheme: 18 (a) 3 2 10 − −2 M1 for or better 4( −0) (b) [y =] 3x – 2 1 ft their (a) x – 2 (c) [y =] 3x 1 ft follow through gradient from their (b) or their (a) √ 2 2

This question in 0580/11 Oct/Nov 2012

19 For Examiner′s y Use 8 7 6 5 4 A 3 2 1 x 0 1 2 3 4 The point A (1, 3.5) is plotted on the grid. (a) Plot the point B (3, 6.5) and draw the straight line through A and B. [1] (b) (i) Find the gradient of the line in part (a). Answer(b)(i) … [2] (ii) Write down the equation of the line in the form y = mx + c. Answer(b)(ii) y = … [2] (c) On the grid, draw a line through the point (2, 5) that is perpendicular to the line in part (a). [1] _____________________________________________________________________________________

6 marks

Mark scheme: 19 (a) B (3 , 6.5) plotted and a ruled line A to B 1 Rise (b) (i) 1.5 oe 2ft M1 for applied to their line Run (ii) (y = ) 1.5 x + 2 2ft B1 for their (b) (i) x + a ( a ≠ 2) or b x + their 2 (b ≠ 0 or 1.5) (c) Ruled Line perpendicular to their line 1ft (±2º) and through the point (2 , 5) IGCSE – May/June 2013 0580 13

This question in 0580/13 May/June 2013

18 For Examiner′s Use A P B C (a) On the diagram above, draw a line perpendicular to the line AB, through the point P. [1] (b) Using a straight edge and compasses only, construct the locus of points that are equidistant from A and from C. [2] _____________________________________________________________________________________

3 marks

Mark scheme: 18 (a) Ruled perpendicular line 1 ± 2° through P (b) Correct ruled line drawn 2 B1 for correct line without correct arcs with 2 correct sets of arcs or for 2 sets of correct arcs with no line h M1 f i 56 b tt

This question in 0580/11 Oct/Nov 2013

14 The straight line, L, has the equation y = 5 – 2x . Write down (a) the co-ordinates of the point where the line crosses the y-axis, Answer(a) ( … , … ) [1] (b) the gradient of the line, Answer(b) … [1] (c) the equation of a line parallel to L. Give your answer in the form y = mx + c. Answer(c) y = … [1] _____________________________________________________________________________________

3 marks

Mark scheme: 14 (a) (0, 5) 1 (b) –2 1 (c) y = –2x + k 1 k ≠ 5

This question in 0580/12 Oct/Nov 2013

12 (a) Write down the co-ordinates of the point where the line y = 3x + 5 crosses the y-axis. Answer(a) ( … , … ) [1] (b) Write down the equation of a line that is parallel to the line y = 3x + 5. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 12 (a) ( 0 , 5 ) 1 (b) y = 3x + k 1 k must be a number, ≠ 5

This question in 0580/11 May/June 2015

16 y 4 l 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 –3 –4 Write down the equation of line l. Give your answer in the form y = mx + c . y = … [3]

3 marks

Mark scheme: 16 y = 3 x − 1 3 M2 for [ y = ] 3 x + c M1 for rise/run If zero scored, SC1 for [ y = ] kx − 1

This question in 0580/12 Feb/March 2016

16 The equation of line L is y = 4x – 3. Write down (a) the co-ordinates of the point where the line L crosses the y-axis, ( … , … ) [1] (b) the gradient of the line L, … [1] (c) the equation of the line parallel to line L that passes through the origin. … [1]

3 marks

Mark scheme: 16 (a) (0, –3) 1 (b) 4 1 (c) y = 4x [+0] 1FT FT y = their (b)x for numerical gradient only

This question in 0580/12 May/June 2016

18 y 7 6 L 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 (a) Work out the gradient of the line L. … [2] (b) Write down the equation of the line parallel to the line L that passes through the point (0, 6). … [2]

4 marks

Mark scheme: 18 (a) 2 cao 2 M1 for rise/run attempted e.g. 4/2 or other correct method for finding gradient or SC1 for y = 2x – 1 as answer (b) y = 2x + 6 oe 2FT FT for y = their(a)x + 6 B1 for y = mx + 6 (m ≠ 0 or 2) or y = 2x [+ k] or y = their(a)x [+ k] (k ≠ 6) or for answer 2x + 6 or answer their(a)x + 6

This question in 0580/13 May/June 2016

23 y l 5 4 3 2 1 x 0 –3 –2 –1 1 2 3 4 5 –1 –2 –3 (a) Find the equation of the line l. Give your answer in the form y = mx + c. y = … [3] (b) Draw another straight line on the diagram that passes through (-1, 1) and is parallel to the line l. [1]

4 marks

Mark scheme: 23 (a) [y =] –2x + 3 3 B2 for [ y = ] − 2 x + c or M1 for rise/run and B1 for [ y = ] kx + 3, k ≠ 0 or c = 3 (b) Ruled line y = −2 x − 1 drawn 1

This question in 0580/12 Feb/March 2017

10 Line l has the equation y = 4x - 6. (a) Write down the co-ordinates of the point where line l crosses the y-axis. ( … , … ) [1] (b) Write down the gradient of line l. … [1]

2 marks

Mark scheme: 10(a) (0, −6) 1 10(b) 4 1

This question in 0580/13 May/June 2017

17 AB is a straight line. A B (a) Measure the length of AB. … cm [1] (b) Mark the midpoint of AB. [1] (c) Draw a line perpendicular to AB. [1]

3 marks

Mark scheme: 17(a) 9 1 17(b) Midpoint marked 1 17(c) Perpendicular line drawn 1

This question in 0580/12 Oct/Nov 2017

21 y 5 l 4 3 2 1 x –2 –1 0 1 2 3 4 5 6 Find the equation of the line l in the form y = mx + c. y = … [3]

3 marks

Mark scheme: 21 [y =] 0.5x + 2 oe 3 M2 for [y =] 0.5x + c oe c ≠ 2 rise or M1 for run and B1 for kx + 2, k ≠ 0

This question in 0580/12 Oct/Nov 2017

20 (a) Line L has the equation y = 5x + 12 . Write down the gradient of line L. … [1] (b) Another line, M, has the equation y = 8x + 3 . Write down the equation of the line parallel to line M that passes through the point (0, 6). … [2]

3 marks

Mark scheme: 20(a) 5 1 20(b) y = 8x + 6 2 M1 for y = 8x + k, k ≠ 3 or 6 or y = mx + 6, m ≠ 0 or 8 or for answer of 8x + 6

This question in 0580/13 May/June 2018

20 y 4 3 L A 2 1 −4 −3 −2 −1 0 1 2 3 4 x −1 −2 −3 −4 (a) Write down the co-ordinates of point A. ( … , … ) [1] (b) On the grid, plot point B (1, –3). [1] (c) Find the gradient of line L. … [2] (d) Find the equation of line L in the form y = mx + c . y = … [1]

5 marks

Mark scheme: 20(a) –3, 2 1 20(b) B plotted at (1, –3) 1 20(c) 1 2 Rise 2 2 −− 1 or 0.5 M1 for e.g. or 2 Run 4 2 −− 4 20(d) 1 1 FT their (c) e.g.[ y =] their (c) x + 1 oe y = x + 1 oe 2

This question in 0580/12 Oct/Nov 2018

16 For the line y = 4x - 6 , write down (a) the gradient, … [1] (b) the y-intercept. … [1]

2 marks

Mark scheme: 16(a) 4 cao 1 16(b) −6 cao 1

This question in 0580/13 Oct/Nov 2018

22 The diagram shows a point P and a line L. y 4 L 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x P – 1 – 2 – 3 – 4 (a) Write down the co-ordinates of point P. ( … , … ) [1] (b) Find the gradient of line L. … [2] (c) Write down the equation of line L in the form y = mx + c. y = … [2]

5 marks

Mark scheme: 22(a) −3, −1 1 22(b) 1.5 oe 2 6 M1 for rise ÷ run e.g. 4 22(c) [y =] 1.5x − 1 oe 2 B1 for jx – 1 j ≠ 0 or 1.5x + k or their(b)x + k

This question in 0580/11 May/June 2019

4 Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis. ( … , … ) [1]

1 marks

Mark scheme: 4 (0, −8) 1

This question in 0580/13 May/June 2019

20 The line L is shown on the grid. y 5 L 4 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 – 4 – 5 (a) Find the gradient of the line L. … [2] (b) Find the equation of the line L in the form y = mx + c . y = … [1]

3 marks

Mark scheme: 20(a) 1.5 oe nfww 2 rise 9 y 2 − y1 M1 for , e.g. or for 2 run 6 x 2 − x1 points on the line 20(b) 1.5x + 1 1 FT their 1.5

This question in 0580/12 Oct/Nov 2019

22 y 6 L 5 4 3 2 1 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 (a) Find the equation of line L in the form y = mx + c. y = … [2] (b) On the grid, draw a line that is perpendicular to line L. [1]

3 marks

Mark scheme: 22(a) 2x − 3 2 B1 for kx – 3 or 2x + k k ≠ −3 22(b) Ruled line perpendicular to L 1

This question in 0580/11 May/June 2020

23 y 12 L 10 8 6 4 2 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 (a) Find the gradient of line L. … [2] (b) Write down the equation of line L in the form y = mx + c . y = … [1]

3 marks

Mark scheme: 23(a) 3 2 3 k M1 for 1k 23(b) y = 3x – 2 oe 1 FT their (a)

This question in 0580/12 May/June 2020

20 y 12 11 L 10 9 8 7 6 5 4 3 2 1 0 x 1 2 3 4 5 6 Find the equation of line L in the form y = mx + c . y = … [2] Question 21 is printed on the next page.

2 marks

Mark scheme: 20 [y =] 1.5x + 3 final answer 2 rise M1 for using correct values run or B1 for [y =] 1.5x + c or [y =] kx + 3, k ≠ 0 as final answer

This question in 0580/11 Oct/Nov 2020

11 A straight line, l, has equation y = 5 x + 12 . (a) Write down the gradient of line l. … [1] (b) Find the coordinates of the point where line l crosses the x-axis. ( … , … ) [2]

3 marks

Mark scheme: 11(a) 5 1 11(b) ( − 125 oe, 0) 2 M1 for 5x + 12 = 0

This question in 0580/13 Oct/Nov 2020

21 (a) y 5 4 3 2 L 1 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 Find the equation of line L in the form y = mx + c . y = … [2] (b) Find the equation of the line which is • parallel to the line y = 3x - 5 and • passes through the point (0, 17). … [1]

3 marks

Mark scheme: 21(a) 1 2 B1 for −0.5x + c oe or mx + 2 oe (m≠0) −0.5x + 2 or – x + 2 2 21(b) y = 3x + 17 cao 1

This question in 0580/13 May/June 2021

19 y 8 6 L 4 2 x – 3 – 2 – 1 0 1 2 3 – 2 – 4 Find the equation of line L. Give your answer in the form y = mx + c . y = … [3]

3 marks

Mark scheme: 19 [y =] 3x + 2 3 B2 for [y =] 3x + c as answer or M1 for a correct rise/run e.g. 6 ÷ 2 or final answer 8 − 2 2 − 0 or for a suitable right-angled triangle marked on graph with correct values shown for rise and run and B1 for [y =] mx + 2, m ≠ 0 as answer

This question in 0580/11 Oct/Nov 2021

14 y L 0 x Explain why the equation of line L in the diagram cannot be y = x + 2 . … … [1]

1 marks

Mark scheme: 14 The line crosses the y-axis below zero not 1 above oe

This question in 0580/13 Oct/Nov 2022

22 Point A and line L are shown on the grid. y 9 L 8 7 6 5 4 3 2 1 -3 -2 -1 0 1 2 3 x -1 -2 × A -3 -4 (a) Write down the coordinates of point A. ( … , … ) [1] (b) On the grid, plot the point ( - 2 , 4). [1] (c) Find the equation of line L. … [3]

5 marks

Mark scheme: 22(a) (1, –2) 1 22(b) Point plotted at (–2, 4) 1 22(c) y = 2x + 3 oe final answer 3 B2 for 2x + 3 or y = 2x + c or y = mx + 3 m ≠ 0 where m is their gradient or B1 for 2x + c or for mx + 3 m ≠ 0 where m is their gradient

This question in 0580/12 Oct/Nov 2023

17 y 4 3 2 L 1 -2 -1 0 1 2 3 4 x -1 (a) Find the equation of line L in the form y = mx + c . y = … [2] (b) On the grid, draw a line that is perpendicular to line L. [1]

3 marks

Mark scheme: 17(a) 1 2 1 [y =] x + 1 B1 for x + c oe 3 3 or for mx + 1 where m is their gradient m ≠ 0 17(b) Any ruled perpendicular line 1

This question in 0580/13 Oct/Nov 2023

17 The line y = 2x - 5 intersects the line y = 3 at the point P. Find the coordinates of the point P. ( … , … ) [2]

2 marks

Mark scheme: 17 ( 4,3 ) 2 B1 for each or M1 for 3 = 2 x − 5 or better

This question in 0580/12 Feb/March 2024

12 Write down the equation of a line parallel to the line y = 2x . … [1]

1 marks

Mark scheme: 12 y = 2x + k, k ≠ 0 oe 1

This question in 0580/13 Oct/Nov 2024

17 Line L is shown on the grid. y 7 L 6 5 4 3 2 1 0 x 1 2 3 4 5 6 7 8 (a) Find the equation of line L in the form y = mx + c . y = … [2] (b) Line L crosses the x-axis at P. Find the coordinates of P. ( … , … ) [2]

4 marks

Mark scheme: 17(a) 2 1  y = 1 x + 3 final answer B1 for x + c 2 2 or B1 for mx + 3 where m ≠ 0 17(b) ( −6,0 ) 2 B1 for (−6, j) or (k, 0) 1 or M1 for 0 = their x + 3 or better 2

This question in 0580/12 Feb/March 2025