Answer
The slope-intercept form is $y=-\frac{1}{3}x+5$.
Work Step by Step
The given points are
$(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(3,4)$
Slope
$\Rightarrow m=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m=\frac{4-5}{3-0}$
Simplify.
$\Rightarrow m=-\frac{1}{3}$
The point-slope form
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $-\frac{1}{3}$ for $m,$ $0$ for $x_1$ and $5$ for $y_1$.
$\Rightarrow y-5=-\frac{1}{3}(x-0)$
Use distributive property.
$\Rightarrow y-5=-\frac{1}{3}x+0$
Add $5$ to each side.
$\Rightarrow y-5+5=-\frac{1}{3}x+5$
Simplify.
$\Rightarrow y=-\frac{1}{3}x+5$
Hence, the slope-intercept form is $y=-\frac{1}{3}x+5$.
