Which best describes the effect on the graph of f(x) = 2x + 6 if the y-intercept is changed to -5?

A. The slope decreases.
Incorrect. The slope is the coefficient of x and affects the steepness.

B. The slope increases.
Incorrect. The slope is the coefficient of x and affects the steepness.

C. The x-intercept increases.
Correct! The x-intercept changes from -3 to 2.5.

D. The new line passes through the origin.
Incorrect. The origin is the point (0, 0).

What will happen to the slope of line a if the line is shifted so that the y-intercept decreases 2 units and the x-intercept remains the same?

A. The slope will change from negative to positive.
Incorrect. If the slope changes from negative to positive, the line will change directions.

B. The slope will change from positive to negative.
Incorrect. If the slope changes from positive to negative, the line will change directions.

C. The slope will increase.
Incorrect. An increase in slope will cause a line to be steeper.

D. The slope will decrease.
Correct! The line will be less steep and so the slope will decrease.

Which best describes the effect on the x-intercept of the graph of f(x) = – 2 3x − 3 if the slope is changed to 2 3?

A. The x-intercept remains the same, and the new line is translated upward.
Incorrect. The y-intercept does not change.

B. The x-intercept becomes positive, and the new line intersects the original line.
Correct! Changing the slope from negative to positive will cause the 2 lines to intersect.

C. The x-intercept becomes negative, and the new line is parallel to the original line.
Incorrect. Parallel lines have the same slope.

D. The x-intercept remains the same, and the new line is translated downward.
Incorrect. The y-intercept does not change.

The line represented by the equation y = x − 4 is graphed below.

Which of the following best describes the effect on the graph when the slope is doubled?

A. The x-intercept decreases.
Correct! The change in slope will cause the x-intercept to decrease.

B. The y-intercept increases.
Incorrect. The y-intercept will not be affected by a change in the slope.

C. Water evaporates at a rate of about 2 gallons per day.
Incorrect. You are reading the labels on the axis incorrectly.

D. Water evaporates at a rate of about 1 gallon per day.
Incorrect. The water is evaporating at a rate of 4 gallons per day.

The graph of a linear function is shown below.

If the line is translated 4 units down, which equation will best describe the new line?

y = 2x + 7
Incorrect. The graph should be shifted down 4 units.

B. y = 1 2x + 7
Incorrect. The graph should be shifted down 4 units.

y = 2x − 1
Incorrect. The graph should be shifted down 4 units.

D. y = 1 2x − 1
Correct! The slope of the translated line will be 1 2 and the y-intercept will be -1.