Question

When graphing a linear equation that is written in the form $y=mx+b$, the variable m represents the slope of the line and b represents the y-intercept. assuming that b>0, which of the following best describes how reversing the sign of b would affect the graph

• A. The new line will shifted down b units.
• B. The new line will be shifted down $b\times 2$ units.
• C. The new line will be perfect reflection across the x-axis.
• D. The new line will be a perfect reflection across the y-axis.

Answer 1

The correct option is B The new line will be shifted down $b\times 2$ units.

Equation of the old line : $y=mx+b$,

Equation of the new line : $y=mx-b$.

We note that if $(p,q)$ is a point on the old line, then $(p,q-2b)$ is on the new line. Conversely, if $(r,s)$ is a point on the new line, then $(r,s+2b)$ is a point on the old line.

This observation allows us to conclude that the entire line is shifted down by b $\times$ 2 units.