Gradient and Intercept: Master Linear Equations with Interactive Quizzes

Question 1

Which of the following equations represents a line with a gradient of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

y = -3x + 2

Question 2

What is the gradient of a line that passes through the points (2, 5) and (4, 9)?

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 3

Which of the following statements is true about a line with a gradient of 0?

Accepted Answer

It is parallel to the x-axis.

Answer

It is a vertical line.

Answer

It has a positive y-intercept.

Answer

It has a negative y-intercept.

Question 4

What is the equation of a line that is vertical and passes through the point (5, -2)?

Accepted Answer

x = 5

Answer

y = 5

Answer

x = -2

Answer

y = -2

Question 5

What is the equation of a line that has a gradient of 2 and passes through the point (1, 3)?

Accepted Answer

y = 2x + 3

Answer

y = 2x + 1

Answer

y = 3x + 1

Answer

y = 3x + 3

Question 6

Which of the following expressions provides the gradient of the straight line represented by the equation y = 2x + 3?

Accepted Answer

2

Answer

0

Answer

3

Answer

-2

Question 7

Calculate the gradient of the line passing through the points (2, 5) and (4, 9).

Accepted Answer

2

Answer

1

Answer

4

Answer

-1

Question 8

Write the equation of the line that has a gradient of -3 and a y-intercept of 2.

Accepted Answer

y = -3x + 2

Answer

y = 3x - 2

Answer

x = -3y + 2

Answer

x = 3y - 2

Question 9

Which equation represents a line that passes through the origin?

Accepted Answer

y = 3x

Answer

y = 2x + 1

Answer

y = -x + 2

Answer

y = 4x - 3

Question 10

Identify the intercept of the line defined by the equation 2x + 3y = 6.

Accepted Answer

2

Answer

3

Answer

-2

Answer

0

Question 11

Which of the following equations represents a line with a gradient of -1 and a y-intercept of 2?

Accepted Answer

y = -x + 2

Answer

y = x + 2

Answer

y = -x - 2

Answer

y = x - 2

Question 12

Determine the gradient and intercept of the line represented by the equation y = 2x - 3.

Accepted Answer

Gradient: 2, Intercept: -3

Answer

Gradient: -2, Intercept: 3

Answer

Gradient: 3, Intercept: -2

Answer

Gradient: -3, Intercept: 2

Question 13

Identify the characteristics of the line with equation y = 2x - 3.

Accepted Answer

Positive gradient, negative intercept

Answer

Zero gradient, negative intercept

Answer

Negative gradient, positive intercept

Question 14

Given that the point (3, 4) lies on the line y = mx + c, determine the value of m.

Accepted Answer

1

Answer

-1

Answer

2

Answer

0

Question 15

Identify the common feature of the parallel lines y = 2x + 1 and y = 2x + c.

Accepted Answer

Gradient

Answer

Intercept

Answer

y-coordinate of the point of intersection

Answer

x-coordinate of the point of intersection

Question 16

Calculate the area of the triangle formed by the x-axis, the y-axis, and the line y = 2x + 1.

Accepted Answer

1/2

Answer

1

Answer

4

Answer

2

Question 17

A line has a gradient of 2 and a y-intercept of -3. Express its equation in the form y = mx + c.

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 3x - 2

Answer

y = -3x + 2

Question 18

Find the equation of a line that is perpendicular to the line y = 2x + 3 and passes through the point (1, 4).

Accepted Answer

y = -1/2x + 5/2

Answer

y = -2x + 5

Answer

y = 1/2x + 3/2

Answer

y = 2x + 1

Question 19

Which line has the steepest gradient?

Accepted Answer

y = 3x - 2

Answer

y = -2x + 4

Answer

y = 2x + 1

Answer

y = -x + 3

Question 20

A line has a gradient of -1/3 and a y-intercept of 5. Write its equation.

Accepted Answer

y = -1/3x + 5

Answer

y = 3x + 5

Answer

y = -3x + 5

Answer

y = 1/3x + 5

Question 21

A line is represented by the equation y = mx + c. If its gradient is multiplied by 2, determine the new equation of the line.

Accepted Answer

y = 2mx + c

Answer

y = mx/2 + c

Answer

y = mx + 2c

Answer

y = 2mx + 2c

Question 22

Determine the equation of the line having a gradient of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

y = -3x + 2

Question 23

Calculate the gradient of the line that passes through the points (2, 5) and (6, 11).

Accepted Answer

2

Answer

-2

Answer

3

Answer

1

Question 24

Identify the line that is parallel to the x-axis.

Accepted Answer

y = 3

Answer

y = 2x + 1

Answer

y = -x + 5

Answer

y = 4x - 2

Question 25

Construct the equation of the line that passes through the point (1, 2) with a gradient of -1.

Accepted Answer

y = -x + 3

Answer

y = x + 3

Answer

y = -x + 1

Answer

y = x + 1

Question 26

Find the equation of the line that passes through the origin and has a gradient of 2.

Accepted Answer

y = 2x

Answer

y = x

Answer

y = 2x + 1

Answer

y = x + 2

Question 27

Select the graph that represents a line with a positive gradient and a negative y-intercept.

Accepted Answer

[Image of a graph with an upward sloping line passing through the y-axis below the origin]

Answer

[Image of a graph with an upward sloping line passing through the y-axis above the origin]

Answer

[Image of a graph with a downward sloping line passing through the y-axis below the origin]

Question 28

Which of the following is the equation of a line with gradient 3 and y-intercept 2?

Accepted Answer

y = 3x + 2

Answer

x = 3y + 2

Answer

y = 2x + 3

Answer

x + y = 5

Question 29

Write the equation of a line perpendicular to y = 2x + 1.

Accepted Answer

y = -(1/2)x + b

Answer

y = 2x + b

Answer

x = 2y + b

Answer

y = (1/2)x + b

Question 30

Identify the gradient of the line with the equation y = mx + c.

Accepted Answer

m

Answer

-m

Answer

-1/m

Answer

1/m

Question 31

Identify the equation of a line parallel to the x-axis.

Accepted Answer

y = 3

Answer

x = 3

Answer

x + y = 3

Answer

y = 3x

Question 32

What does the gradient of a straight line tell us about the line?

Accepted Answer

How steep the line is and whether it slopes upwards or downwards

Answer

The curvature of the line

Answer

The total length of the line

Answer

Where the line crosses the y-axis

Question 33

Which of these equations is written in gradient-intercept form (y = mx + c)?

Accepted Answer

y = -2x + 5

Answer

x = 4y - 1

Answer

y - 3 = 2(x + 1)

Answer

2x + 3y = 6

Question 34

A line passes through the points (2, 5) and (4, 11). What is its gradient?

Accepted Answer

3

Answer

-1/3

Answer

-3

Answer

1/3

Question 35

What is the y-intercept of the line represented by the equation y = 3x - 2?

Accepted Answer

-2

Answer

3

Answer

2

Answer

-3

Question 36

A line has a gradient of -2 and passes through the point (1, 4). What is its equation in gradient-intercept form?

Accepted Answer

y = -2x + 6

Answer

y = 2x + 2

Answer

y = 2x + 6

Answer

y = -2x + 2

Question 37

Two lines are parallel. What do we know about their gradients?

Accepted Answer

They have the same gradient.

Answer

They have the same y-intercept.

Answer

Their gradients multiply to give -1.

Answer

They have opposite gradients.

Question 38

A line has an equation of y = (1/2)x + 3. Which of the following lines is perpendicular to it?

Accepted Answer

y = -2x + 1

Answer

y = - (1/2)x + 4

Answer

y = 2x + 3

Answer

y = (1/2)x - 2

Question 39

The cost of renting a bike is £10 plus £2 per hour. Which equation represents the total cost (C) for renting the bike for h hours?

Accepted Answer

C = 2h + 10

Answer

C = h/2 + 10

Answer

C = 10h + 2

Answer

C = 12h

Question 40

The graph of a linear function does NOT pass through the origin. What can we say about the function?

Accepted Answer

The y-intercept is not zero.

Answer

The gradient is zero.

Answer

The x-intercept is zero.

Answer

The function is not linear.

Question 41

A line has a gradient of 0. Which of the following describes the line?

Accepted Answer

Horizontal

Answer

Vertical

Answer

Has a negative y-intercept

Answer

Passes through the origin