linear relationships

What is the equation of a straight line in slope-intercept form?

• y = mx + b

• y = kx

• y = x + b

• y = mx

Answer explanation

The equation of a straight line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

In a direct variation, what is the relationship between the two variables?

• One variable is a constant multiple of the other

• One variable is a constant addition to the other

• One variable is a constant subtraction from the other

• One variable is a constant division of the other

Answer explanation

In a direct variation, one variable is a constant multiple of the other, meaning they change proportionally.

What does the y-intercept represent in the equation of a straight line?

• The point where a line crosses the y-axis

• The point where a line crosses the x-axis

• The slope of the line

• The constant ratio of the line

Answer explanation

The y-intercept represents the point where a line crosses the y-axis, making it the correct choice.

Which of the following is a common mistake students make regarding proportional relationships?

• Mistaking the meaning of "proportional" with other familiar terms such as linear or function

• Confusing the y-intercept with the slope

• Using the wrong formula for slope

• Forgetting to label the axes on a graph

Answer explanation

Students commonly mistake the meaning of 'proportional' with terms like linear or function, which is the correct answer choice.

What is a linear relationship?

• A relationship that can be represented with a straight line that has a constant rate of change or slope

• A relationship where one variable is a constant multiple of the other

• A relationship with a constant ratio that passes through the origin

• A relationship that forms a curve on a graph

Answer explanation

A relationship that can be represented with a straight line that has a constant rate of change or slope

Write an equation in slope-intercept form to represent the total cost of a cab ride (y) for a certain number of miles (x).

• y = 3x + 3

• y = 3x + 2

• y = 3x + 1

• y = 3x + 0.5

Answer explanation

The correct equation in slope-intercept form is y = 3x + 2, where the slope is 3 and the y-intercept is 2, representing the total cost of a cab ride for a certain number of miles.

At what rate is the tree growing according to the graph?

• 2 ft/year

• 3 ft/year

• 4 ft/year

• 5 ft/year

Answer explanation

The tree is growing at a rate of 4 ft/year according to the graph, as shown by the slope of the line.

Is the graph showing the height of the tree proportional?

• Yes

• No

• Cannot be determined

• Only for the first 5 years

Answer explanation

The correct answer is 'No' because the graph does not show a proportional relationship between the height of the tree and time.

What is the slope-intercept form of a linear equation?

• y = mx + b

• y = bx + m

• y = m + bx

• y = b + mx

Answer explanation

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Therefore, the correct choice is y = mx + b.

If a line has a slope of 8 and a y-intercept of -10, what is the equation of the line?

• y = 8x + 10

• y = 8x - 10

• y = -8x + 10

• y = -8x - 10

Answer explanation

The correct equation of the line with a slope of 8 and a y-intercept of -10 is y = 8x - 10, as the slope is the coefficient of x and the y-intercept is the constant term.