Graphs 2

3 marks · Normal

A straight line passes through the points $A(3, 5)$ and $B(7, 13)$.

Find the equation of the line in the form $y = mx + c$.

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y = 2x - 1

Also accept: y=2x-1; y = 2x -1

Common mistakes: y = 2x + 1

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Calculates correct gradient: (13 - 5)/(7 - 3) = 2.

M2 · 1 mark · Substitutes (3, 5) or (7, 13) into y = 2x + c to solve for c.

A1 · 1 mark · States y = 2x - 1 as the final answer.

Worked solution

Gradient $m = (13 - 5)/(7 - 3) = 8/4 = 2$.

$y = 2x + c$; substitute $A(3, 5) \Longrightarrow 5 = 2\times3 + c \implies 5 = 6 + c \implies c = -1$.

Equation is $y = 2x - 1$.