Question

What happens to a line when the y-intercept is changed? Check all that apply.

Answer 1

Answer:

As the y-intercept increases, the graph of the line shifts up;

As the y-intercept decreases, the graph of the line shifts down

Explanation:

There are two ways to think about this problem. The first way would be the graphical approach:

• if we only change the y-intercept, this means we keep the same slope;
• y-axis is the vertical axis;
• if we change the point at which the line crosses the y-axis, we either shift it upward for a higher y-intercept or downward for a lower y-intercept.

Now, thinking algebraically, a line has the following equation in a general form:

$y = mx + b$

The y-intercept is essentially obtained when x = 0, then:

y = b:

• if we increase b value, the y value increases, so the graph shifts upward;
• if we decrease b value, the y value decreases, so the graph shifts downward.