**Question** Using y = 3x + 1, find the equation of a second line by multiplying the slope by 2 and shifting the line down by 3 units.

You are watching: What happens to a line when the y-intercept is changed

Answer**STEP 1: **You are given the equation of a line to be used it to find the equation of another line which has double the slope and is vertically shifted downwards.**Start working by finding the slope of the given line. Since the equation is already in the slope-intercept form (y = mx + b**), you can easily find the slope.**Make a note of what each variable in the equation stands for:**

**You also have the value of the y-intercept from the comparison as 1. The corresponding point is (0, 1). Now, if the line gets shifted downwards by 3 units, there will also be a change in its y-coordinate. It gets reduced by 3 units.**

STEP 2:

STEP 2:

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**Now, the only step left is to substitute for m and b in the slope-intercept form.**

The new coordinate point is (0, –2), and hence the new y-intercept is –2.STEP 3:

The new coordinate point is (0, –2), and hence the new y-intercept is –2.STEP 3:

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