Equation of a line

Foundation and Higher

The idea

To write the equation of a line, find its gradient $m$ , then use a point on it to find $c$ in $y = mx + c$ . Parallel lines have the same gradient.

Watch out $c$ is where the line crosses the $y$ -axis, not the $x$ -axis.

Worked exampleNon-calculator3 marks

Answer each part.

(a) Write down the equation of the line that is parallel to $y = 3x + 2$ and passes through $(0, -5)$ .

(b) Which line is parallel to $y = 4x - 1$ ?

(a) Parallel lines have the same gradient, 3. The line passes through $(0, -5)$ , so it crosses the $y$ -axis at $-5$ : $y = 3x - 5$ .
(b) Parallel lines have equal gradients. Only $y = 4x + 3$ has gradient 4.

Answer (a) $y = 3x - 5$ ; (b) $y = 4x + 3$

Question 1Non-calculator3 marks

A straight line has gradient $-1$ and passes through $(0, 2)$ .

(a) Write down the equation of the line.

(b) Does the point $(5, -3)$ lie on the line? You must show how you get your answer.

Question 2Non-calculator4 marks

A straight line passes through the points (−3, 11) and (2, 1).

(a) Find the gradient of the line.

(b) Find the equation of the line in the form y = mx + c.

Question 3Non-calculator5 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 $L_2$ .

(b) Find the coordinates of the point where $L_2$ crosses the $x$ -axis.

74 official questions in 70 papers since 2017. The latest:

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