Question

consider the graph of the linear function $h(x) = -\frac{2}{3}x + 5$. 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 slope-intercept form

The slope - intercept form of a linear function is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the function \(h(x)=-\frac{2}{3}x + 5\), \(m =-\frac{2}{3}\) and \(b = 5\).

Step2: Analyze vertical shift

Moving a graph down 3 units vertically affects the y - intercept (\(b\)) of the linear function. The new y - intercept \(b_{new}\) should be \(b_{old}-3\). Since \(b_{old} = 5\), then \(b_{new}=5 - 3=2\). The slope (\(m\)) of a linear function affects the steepness and direction of the line, not the vertical shift. So we need to change the value of \(b\) to 2.

Answer:

the value of \(b\) to 2