Worksheets · Foundation and Higher

Equations of lines and parallel lines

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
Answer each part.
(a) Write down the equation of the line that is parallel to $y = 3x + 2$ and passes through $(0, -5)$ . (2)
(b) Which line is parallel to $y = 4x - 1$ ? (1)
1. $y = 4x + 3$
2. $y = x - 1$
3. $y = -4x - 1$
4. $y = \frac{1}{4}x$
Question 2Non-calculator · 4 marks
Lines L1 and L2 have equations $y = 3x - 2$ and $6x - 2y = 7$ .
(a) Show that L1 and L2 are parallel. (2)
(b) Find the coordinates of the point where L2 crosses the x-axis. (2)
Question 3Non-calculator · 5 marks
Line $L_1$ has equation $2y - 6x = 8$ . Line $L_2$ is parallel to $L_1$ and passes through the point $(4, 5)$ .
(a) Find an equation of $L_2$ . (3)
(b) Find the coordinates of the point where $L_2$ crosses the $x$ -axis. (2)

Answers and marks

(a) $y = 3x - 5$

(b) $y = 4x + 3$

(a) L2 rearranges to y = 3x - 3.5, so both lines have gradient 3.

M1 Rearrange L2 into the form y = mx + c.
C1 Correct conclusion with supporting reasoning: L2 rearranges to y = 3x - 3.5, so both lines have gradient 3.

(b) $(7/6,0)$

(a) $y = 3x - 7$

(b) $\left(\frac{7}{3}, 0\right)$

Equations of lines and parallel lines

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