Graphs 4
4 marks · HardConsider the straight line with equation .
For what value of does this line pass through the point (2, 7)?
Find the gradient and explain its meaning in the context of any straight line graph.
Calculate the x-coordinate where the line crosses the x-axis.
Given a second line with equation , what value of would make the two lines parallel and intersect at y = 10?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) c = -3
(b) Gradient is 5; means for each unit increase in x, y increases by 5.
(c) x = -c/5
(d) d = 10
Must show: Gradient definition, Correct use of coordinates
Common mistakes: Mixing up c and d; Incorrectly solving for x or y
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Substitute (2,7): 7 = 10 + c ⇒ c = -3.
B1 (b) · 1 mark · Gives correct gradient, links to rate of change (for each 1 unit change in x, y changes by 5).
A2 (c) · 1 mark · Solves y=0: 0=5x + c ⇒ x= -c/5.
A3 (d) · 1 mark · If y=10 on both lines, set y=10=5x+d (for any x), so d=10.
Worked solution
(a) Substitute (2,7) into y = 5x + c: 7 = 5\times2 + c → c = 7 - 10 = -3.
(b) The gradient is 5: for each unit increase in x, y increases by 5 units; it represents the rate of change of y with respect to x.
(c) y = 0 when the line crosses the x-axis: 0 = 5x + c ⇒ x = -c/5.
(d) For lines to be parallel, gradient must be equal. For both to intersect y = 10, d must equal 10.