Equation of a line

Write the equation of a line given gradient and y-intercept, find the equation from two points, and determine equations of parallel lines.

Worked examples

Writing the equation of a line from gradient and y-intercept

Straightforward

Problem

Write the equation of a line with gradient

m = 3

and y-intercept

b = -4

Finding the equation of a line from two points

Moderate

Problem

Find the equation of the line passing through

(1, 2)

and

(4, 11)

Finding the equation of a line parallel to a given line

Challenging

Problem

Find the equation of the line that is parallel to

y = 2x - 3

and passes through the point

(4, 11)

Practise

Open Math

Equation of a line

Algebra · MA4-LIN-C-01

Name:

Date:

Q1Straightforward

A line has gradient

m = 3

and y-intercept

b = 2

. Which of the following is the equation of the line?

A. $y = 2x + 3$
B. $y = 3x + 2$
C. $y = 3x - 2$
D. $y = 2x - 3$

Q2Straightforward

A line has gradient

m = -2

and y-intercept

b = 5

. Which of the following is the equation of the line?

A. $y = 5x - 2$
B. $y = -2x - 5$
C. $y = 2x + 5$
D. $y = -2x + 5$

Q3Straightforward

A line has gradient

m = \dfrac{1}{2}

and y-intercept

b = -3

. Which of the following is the equation of the line?

A. $y = -3x + \dfrac{1}{2}$
B. $y = \dfrac{1}{2}x + 3$
C. $y = 2x - 3$
D. $y = \dfrac{1}{2}x - 3$

Q4Straightforward

A line has gradient

m = -1

and passes through the origin. Which of the following is the equation of the line?

A. $y = x$
B. $y = -x + 1$
C. $y = -x$
D. $y = x - 1$

Q5Moderate

A line passes through

(1, 3)

and

(4, 9)

. Find the gradient of the line.

Q6Moderate

A line passes through

(1, 3)

and

(4, 9)

. The gradient is

2

. Find the y-intercept of the line.

Q7Moderate

A line passes through

(1, 4)

and

(3, -2)

. Find the y-intercept of the line.

Q8Moderate

A line passes through

(-1, 1)

and

(2, 7)

. Which of the following is the equation of the line?

A. $y = 3x + 2$
B. $y = 2x + 3$
C. $y = 2x - 3$
D. $y = 3x - 2$

Q9Challenging

Line A is

y = 4x + 1

and Line B is

y = 4x - 7

. Which statement best describes the two lines?

A.They are parallel because they have equal gradients.
B.They are the same line because their equations look similar.
C.They are not parallel because they have different y-intercepts.
D.They are perpendicular because their y-intercepts add to $-6$ .

Q10Challenging

Find the y-intercept of the line that is parallel to

y = 2x + 5

and passes through the point

(3, 10)

Q11Challenging

Which of the following lines is parallel to

y = -3x + 2

A. $y = 3x + 2$
B. $y = -2x + 3$
C. $y = -3x - 4$
D. $y = 3x - 4$

Q12Challenging

Find the y-intercept of the line that is parallel to

y = -2x + 1

and passes through the point

(4, 3)

Worked solutions and answers at openmath.au/year-8/linear-relationships/equation-of-a-line