Equation of a line

Q1·Straightforward

A line has gradient

m = 3

and y-intercept

b = 2

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

$y = 2x + 3$$y = 3x + 2$$y = 3x - 2$$y = 2x - 3$

Q2·Straightforward

A line has gradient

m = -2

and y-intercept

b = 5

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

$y = 5x - 2$$y = -2x - 5$$y = 2x + 5$$y = -2x + 5$

Q3·Straightforward

A line has gradient

m = \dfrac{1}{2}

and y-intercept

b = -3

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

$y = -3x + \dfrac{1}{2}$$y = \dfrac{1}{2}x + 3$$y = 2x - 3$$y = \dfrac{1}{2}x - 3$

Q4·Straightforward

A line has gradient

m = -1

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

$y = x$$y = -x + 1$$y = -x$$y = x - 1$

Q5·Moderate

A line passes through

(1, 3)

and

(4, 9)

. Find the gradient of the line.

Q6·Moderate

A line passes through

(1, 3)

and

(4, 9)

. The gradient is

2

. Find the y-intercept of the line.

Q7·Moderate

A line passes through

(1, 4)

and

(3, -2)

. Find the y-intercept of the line.

Q8·Moderate

A line passes through

(-1, 1)

and

(2, 7)

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

$y = 3x + 2$$y = 2x + 3$$y = 2x - 3$$y = 3x - 2$

Q9·Challenging

Line A is

y = 4x + 1

and Line B is

y = 4x - 7

. Which statement best describes the two lines?

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

Q10·Challenging

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

y = 2x + 5

and passes through the point

(3, 10)

.

Q11·Challenging

Which of the following lines is parallel to

y = -3x + 2

?

$y = 3x + 2$$y = -2x + 3$$y = -3x - 4$$y = 3x - 4$

Q12·Challenging

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

y = -2x + 1

and passes through the point

(4, 3)

.

Equation of a line

Worked examples

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

Finding the equation of a line from two points

Finding the equation of a line parallel to a given line

Practise