Gradient 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

15 y 3 l 2 B 1 x –4 –3 –2 –1 0 1 2 3 4 –1 –2 –3 (a) Mark clearly on the diagram the point with co-ordinates (3, 2) and label it A. [1] (b) Write down the co-ordinates of the point B. Answer(b) ( , ) [1] (c) Find the gradient of the line l. Answer(c) [1]

3 marks

Mark scheme: 15 (a) Point marked at (3, 2) 1 Missing label not penalised. (b) ( −2, 1) 1 More than 1 point seen, must be labelled (c) 1 1 By eye 2mm −0.5 or − 2

This question in 0580/11 Oct/Nov 2008

6 (a) Write down the gradient of the line y = 3x – 4. Answer(a) [1] (b) Write down the equation of a line through (0, 0) parallel to y = 3x – 4. Answer(b) [1]

2 marks

Mark scheme: 6 (a) 3 1cao (b) y = 3x oe 1ft Allow y = 3x + 0 or y = 3x − 0 Must be an equation. i.e. y = …..

This question in 0580/11 May/June 2009

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

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

8 y NOT TO P SCALE l x 0 The equation of the line l in the diagram is y = 5 – x . (a) The line cuts the y-axis at P. Write down the co-ordinates of P. Answer(a) ( … , … ) [1] (b) Write down the gradient of the line l. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 8 (a) (0, 5) 1 (b) – 1 1

This question in 0580/12 May/June 2014

21 (a) y 8 7 B 6 5 4 3 2 1 A x 0 0.5 1 1.5 2 2.5 3 The line AB is drawn on the grid. (i) Write down the co-ordinates of A. ( … , … ) [1] (ii) Work out the gradient of the line AB. … [2] (iii) Write down the equation of the line AB in the form y = mx + c. y = … [2] (b) Write down the equation of a straight line that is parallel to y = 5x – 3. … [1]

6 marks

Mark scheme: 21 (a) (i) 0, 1 1 (ii) 2 2 M1 for a correct rise ÷ run e.g. 4 ÷ 2 or for right-angled triangle marked on graph with run = 1 and rise = 2 oe (iii) [y =] 2x + 1 final answer 2FT FT their (a)(i) for c and their (a)(ii) for m B1 for y = 2x + c ( c ≠ 1) or y = mx + 1 (m ≠ 2 or 0) (b) y = 5x + c oe final answer 1 where c ≠ −3

This question in 0580/11 May/June 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

16 y 7 A 6 5 4 3 2 B 1 x 0 1 2 3 4 5 6 7 8 Point A has co-ordinates (3, 6). (a) Write down the co-ordinates of point B. ( … , … ) [1] (b) Find the gradient of the line AB. … [2]

3 marks

Mark scheme: 16 (a) (7 , 1) 1 5 1 (b) –1.25 or − or − 2 M1 for rise/run 4 14

This question in 0580/12 Oct/Nov 2016

17 y B 10 9 8 7 6 5 4 3 2 1 A x 0 1 2 3 4 5 Find the gradient of the line AB. … [2]

2 marks

Mark scheme: 17 3 cao 2 M1 for rise ÷ run

This question in 0580/12 May/June 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

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

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

9 (a) Write down the gradient of the line y = 2x - 3 . … [1] (b) Complete the table of values for y = 2x - 3 . x -2 0 3 y [2] (c) On the grid, draw the graph of y = 2x - 3 for - 2 G x G 3 . y 4 2 – 2 – 1 0 1 2 3 x – 2 – 4 – 6 – 8 [1]

4 marks

Mark scheme: 9(a) 2 1 9(b) – 7 – 3 3 2 B1 for 2 correct 9(c) Correct ruled graph 1 FT their (b) provided it is a single ruled straight line

This question in 0580/12 Feb/March 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

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

13 The equation of a line is y = 5 x + 7 . (a) Write down the gradient of this line. … [1] (b) (i) Find the coordinates of the point where this line crosses the y-axis. ( … , … ) [1] (ii) Find the coordinates of the point where this line crosses the x-axis. ( … , … ) [2]

4 marks

Mark scheme: 13(a) 5 1 13(b)(i) (0, 7) 1 13(b)(ii)  7  2 B1 for 0 = 5 x + 7 oe  − , 0  oe  5 

This question in 0580/12 Feb/March 2022

2 B A (a) Measure the length of the line AB in millimetres. … mm [1] (b) Mark the midpoint, M, of the line AB. [1] (c) Draw a line through M that is perpendicular to the line AB. [1]

3 marks

Mark scheme: 2(a) 86 1 2(b) Point marked at 4.3 cm from A 1 2(c) Ruled line through M perpendicular to 1 AB

This question in 0580/13 May/June 2022

20 y 4 3 L 2 1 – 3 – 2 – 1 0 1 2 x – 1 – 2 – 3 – 4 – 5 – 6 Find the gradient of line L. … [2]

2 marks

Mark scheme: 20 −2 2 k2 M1 for 1k y 2  y1 or for for 2 points on the line x2  x1

This question in 0580/13 May/June 2022

10 (a) Line A has equation y = 3x + 1. Line B has equation y = 3x - 1. Draw a ring around the description that is correct. Line A intersects Line A has a Line A is line B steeper gradient perpendicular to than line B line B Line A is parallel Line A and Line B to line B intersect the y-axis at the same point [1] (b) y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 On the grid, draw the graph of y = 2x - 1. [2]

3 marks

Mark scheme: 10(a) Circle around the statement 1 Line A is parallel to line B 10(b) Correct graph of y = 2x – 1 2 B1 for short or unruled line or for two correct coordinates plotted or for line with positive gradient passing through (0, –1) or for line with gradient 2

This question in 0580/13 May/June 2025