Unit 11- Linear Equations

Multiple Choice

Which of the following best describes a linear relation?

• A relationship where the graph is a straight line

• A relationship where the graph is a curve

• A relationship that cannot be represented on a graph

• A relationship with no pattern

Open Ended

Why is it important to understand and graph linear relations in mathematics?

Multiple Select

Which of the following are true about the equation y = mx + c?

• The gradient is represented by m

• The y-intercept is represented by c

• The x in the equation has a power of 1

• The equation represents a quadratic function

Fill in the Blank

The y-intercept in the equation y = mx + c is represented by ___

Open Ended

Explain the difference between the gradient and the y-intercept in the equation of a straight line.

Multiple Choice

What does the variable 'm' represent in the equation of a straight line y = mx + c?

• The gradient of the line

• The y-intercept of the line

• The x-intercept of the line

• The midpoint of the line

Multiple Choice

Given the straight line equation y = -6x + 1, what are the gradient and y-intercept?

• Gradient = -6, y-intercept = 1

• Gradient = 1, y-intercept = -6

• Gradient = 6, y-intercept = -1

• Gradient = -1, y-intercept = 6

Open Ended

How can you determine the x-intercept and y-intercept of a straight line from its graph?

Multiple Choice

What is the x-intercept of a line, and what is the y-intercept of a line?

• The x-intercept is where the line crosses the x-axis, and the y-intercept is where the line crosses the y-axis.

• The x-intercept is where the line crosses the y-axis, and the y-intercept is where the line crosses the x-axis.

• The x-intercept is where the line is parallel to the x-axis, and the y-intercept is where the line is parallel to the y-axis.

• The x-intercept and y-intercept are always at the origin.

Fill in the Blank

Given the graph in image 2, what are the coordinates of the x-intercept and y-intercept of the line?

Fill in the Blank

For the line shown in image 3, determine the x-intercept and y-intercept.

Fill in the Blank

For the line shown in image 4, determine the x-intercept and y-intercept.

Open Ended

Explain how you can find the x-intercept and y-intercept of a line from its graph. Use examples from any of the images above to support your explanation.

Fill in the Blank

For the line shown in image 5, determine the x-intercept and y-intercept.

Open Ended

What are the x-intercept and y-intercept of the line shown in the graph?

Multiple Choice

According to the background theory, how do you find the x-intercept and y-intercept of a line algebraically?

• Substitute x = 0 for y-intercept and y = 0 for x-intercept

• Substitute x = 1 for y-intercept and y = 1 for x-intercept

• Substitute x = 0 for x-intercept and y = 0 for y-intercept

• Substitute x = y for both intercepts

Open Ended

Calculate the x and y intercepts for the line given by y = 2x + 6.

Multiple Choice

Which of the following are correct steps to find the x-intercept for the equation y = 2x + 6?

• Set y = 0 and solve for x

• Set x = 0 and solve for y

• Set x = 1 and solve for y

• Set y = 1 and solve for x

Multiple Choice

If a line has the equation y = mx + c, what does the constant c represent?

• The slope of the line

• The x-intercept

• The y-intercept

• The origin

Fill in the Blank

The y-intercept of the line y = -3x + 7 is ___

Multiple Choice

What is the value of y at the x-axis intercept and the value of x at the y-axis intercept for a linear equation?

• At the x-axis intercept, y = 0 and at the y-axis intercept, x = 0.

• At the x-axis intercept, x = 0 and at the y-axis intercept, y = 0.

• At both intercepts, x = y = 0.

• At the x-axis intercept, y = x and at the y-axis intercept, x = y.

Open Ended

Describe the difference between a zero gradient and an undefined gradient in the context of linear graphs.

Multiple Choice

Which type of gradient is represented by a line that moves upward from left to right on a graph?

• Positive gradient

• Negative gradient

• Zero gradient

• Undefined gradient

Open Ended

Explain how you would determine the x-intercept and y-intercept of the line given by the equation y = 6 + 2x without plotting or using a table of values.

Fill in the Blank

Fill in the blank: The x-intercept of the line 5x + 2y = 7 is ( ___ , 0).

Multiple Select

Which of the following are correct results for the given addition and subtraction operations?

• 3 + 4 = 7 (Positive)

• -3 - 4 = -7 (Negative)

• 5 - 2 = 3 (Positive, if the positive is larger)

• -5 + 2 = 3 (Positive, if the positive is larger)

Multiple Choice

Which of these lines has a negative gradient?

• The orange one
• The red one
• The blue one
• The green one

Multiple Choice

What gradient is represented here

• Positive

• negative

• undefined

• zero

Multiple Choice

Find the gradient of the line.

• Undefined

• 0

• 1

• -1

Multiple Choice

Find the gradient of line.

• $$-3$$

• $$3$$

• $$-\frac{1}{3}$$

• $$\frac{1}{3}$$

Multiple Choice

What is the gradient of this line

• 4

• 4/5

• -2

• -1/2

Multiple Choice

What is the gradient of this slope

• 5

• 5/2

• 5/3

• -5/3

Multiple Select

How do you measure gradient?

• Gradient = rise / run

• Gradient = vertical change in x / horizontal change in y

• Gradient = vertical change in y / horizontal change in x

• Gradient = run / rise

Fill in the Blank

State the value of the x - intercept and the value of y - intercept of the straight line AB.

y intercept = _

x intercept = _

=

-

=

Fill in the Blank

State the value of the x - intercept and the value of y - intercept of the straight line AB.

y intercept = _

x intercept = _

=

-

=

-

Multiple Choice

The equation of a graph is y= 4x +1. What is the gradient of the graph?

• +1

• 4

• Positive Gradient

• 5

Multiple Choice

Find the gradient.

• $$\frac{6}{4}$$

• $$-\frac{4}{6}$$

• $$-\frac{3}{2}$$

• $$-\frac{2}{3}$$

Multiple Choice

The gradient of the linear function $$y=3x+7$$  

• $$\left(0,-7\right)$$  

• $$\left(0,7\right)$$  

• $$3$$  

• $$-3$$  

Multiple Choice

The gradient of the linear function $$y=7-3x$$  

• $$\left(0,-7\right)$$  

• $$\left(0,7\right)$$  

• $$3$$  

• $$-3$$  

Open Ended

After revising the topic of straight line graphs, what is one question you still have or something you would like to know more about?

Open Ended

What is one way you can use digital tools to solve problems involving linear relations?