Linear

Question 1

What is the standard form of a linear equation?

Answer 1

y = mx + c

Question 2

In the equation y = mx + c, what does ‘m’ represent?

Answer 2

‘m’ represents the gradient (slope) of the line.

Question 3

In the equation y = mx + c, what does ‘c’ represent?

Answer 3

‘c’ represents the y-intercept of the line.

Question 4

What is the y-intercept of a line?

Answer 4

The y-intercept is the point where the line crosses the y-axis.

Question 5

What is the x-intercept of a line?

Answer 5

The x-intercept is the point where the line crosses the x-axis.

Question 6

True or False: The gradient of a line is the same as its slope.

Answer 6

True

Question 7

What is the gradient of a line that goes upwards from left to right?

Answer 7

The gradient is positive.

Question 8

What is the gradient of a line that goes downwards from left to right?

Answer 8

The gradient is negative.

Question 9

Fill in the blank: A line is ________ if it has a gradient of 0.

Answer 9

horizontal

Question 10

Fill in the blank: A line is ________ if it is vertical.

Answer 10

undefined

Question 11

What does it mean for two lines to be perpendicular?

Answer 11

Two lines are perpendicular if the product of their gradients is -1.

Question 12

What does it mean for two lines to be parallel?

Answer 12

Two lines are parallel if they have the same gradient.

Question 13

If the gradient of a line is 3, what is the gradient of a line perpendicular to it?

Answer 13

-1/3

Question 14

What is the slope of a line represented by the equation 2y - 4x = 8?

Answer 14

The slope is 2.

Question 15

Convert the equation 3x + 2y = 6 to slope-intercept form.

Answer 15

y = -1.5x + 3

Question 16

What is the slope of the line represented by the equation y = -4x + 7?

Answer 16

-4

Question 17

If a line has a slope of 0, what can be said about its direction?

Answer 17

The line is horizontal.

Question 18

If a line has an undefined slope, what can be said about its direction?

Answer 18

The line is vertical.

Question 19

True or False: The x-intercept can be found by setting y = 0 in the equation.

Answer 19

True

Question 20

What is the x-intercept of the line represented by the equation y = 2x - 6?

Answer 20

3

Question 21

Find the y-intercept of the equation y = 5x + 10.

Answer 21

10

Question 22

What is the gradient of the line passing through the points (2, 3) and (4, 7)?

Answer 22

2

Question 23

What formula is used to calculate the gradient between two points (x1, y1) and (x2, y2)?

Answer 23

m = (y2 - y1) / (x2 - x1)

Question 24

True or False: A line can intersect the x-axis at more than one point.

Answer 24

False

Question 25

What is the slope of a line that is perfectly horizontal?

Answer 25

0

Question 26

What is the slope of a line that is perfectly vertical?

Answer 26

undefined

Question 27

What do you call the point (x, 0) on a graph?

Answer 27

x-intercept

Question 28

What do you call the point (0, y) on a graph?

Answer 28

y-intercept

Question 29

If a line has a gradient of 1, what is the angle it forms with the x-axis?

Answer 29

45 degrees

Question 30

What is the relationship between parallel lines in terms of their slopes?

Answer 30

They have equal slopes.

Question 31

What is the relationship between perpendicular lines in terms of their slopes?

Answer 31

The product of their slopes is -1.

Question 32

How can you determine if two lines are parallel from their equations?

Answer 32

Compare their slopes; if they are equal, the lines are parallel.

Question 33

What is the slope of the line given by the equation 4x + 2y = 8?

Answer 33

-2

Question 34

What is the y-intercept of the line represented by the equation y = 3x - 5?

Answer 34

-5

Question 35

What is the significance of the point where a line crosses the y-axis?

Answer 35

It indicates the value of y when x is zero.

Question 36

Convert the equation y - 2 = 3(x - 1) into slope-intercept form.

Answer 36

y = 3x - 1