Question

analyzing the y-intercept
consider the graph of the linear function ( h(x) = -\frac{1}{3}x + 5 ). which could you change to move the graph down 3 units?

• the value of ( b ) to ( -3 )
• the value of ( m ) to ( -3 )
• the value of ( b ) to ( 2 )
• the value of ( m ) to ( 2 )

Explanation:

Step1: Recall linear function form

A linear function is $h(x)=mx+b$, where $b$ is the y-intercept (vertical position), and $m$ is the slope (controls steepness/direction, not vertical shift).

Step2: Calculate new y-intercept

To move the graph down 3 units, subtract 3 from the original $b=5$.
$\text{New } b = 5 - 3 = 2$

Step3: Identify correct change

Changing the slope ($m$) does not shift the graph vertically, so only adjusting $b$ to 2 works.

Answer:

the value of b to 2