Question

investigating the y-intercept
use the slider to change the value of b. which statement is true?

• if the value of b is increased from 0, the graph moves up
• if the value of b is increased from 0, the graph gets less steep
• if the value of b is decreased from 0, the graph moves up.
• if the value of b is decreased from 0, the graph gets steeper

$y = x + b$ $b = 0$

Explanation:

The given equation is $y = x + b$, which is in slope-intercept form $y=mx+b$, where $m=1$ (fixed slope, so steepness never changes) and $b$ is the y-intercept. When $b$ increases, the y-intercept moves upward, shifting the entire line up. When $b$ decreases, the line shifts downward. The slope remains 1, so steepness is unaffected by changes to $b$.

Answer:

A. If the value of $b$ is increased from 0, the graph moves up