Question

1. find the equation of the linear function ( r(x) ) that is parallel to ( h(x) = -\frac{4}{5}x + 11 ) and has the same y - intercept as ( s(x) = 3x + \frac{16}{3} ).

Explanation:

Step1: Identify parallel slope

Parallel lines have equal slopes. For $h(x)=-\frac{4}{5}x+11$, the slope $m=-\frac{4}{5}$.

Step2: Identify target y-intercept

The y-intercept of $s(x)=3x+\frac{16}{3}$ is $b=\frac{16}{3}$.

Step3: Build linear function

Use slope-intercept form $r(x)=mx+b$.
Substitute $m=-\frac{4}{5}$ and $b=\frac{16}{3}$:
$r(x)=-\frac{4}{5}x+\frac{16}{3}$

Answer:

$r(x)=-\frac{4}{5}x+\frac{16}{3}$