We want to write the equation:
[tex]y+6=-\frac{8}{5}(x-9)[/tex]
In slope-intercept form.
The slope-intercept form is given by the equation:
[tex]y=mx+b[/tex]
Where m is the slope, and b is the slope-intercept with y-axis.
Now, we could start by multiplying the number outside the bracket per all the terms inside of it. This is,
[tex]y+6=-\frac{8}{5}x+\frac{72}{5}[/tex]
Now, we could solve the equation for y as follows:
[tex]\begin{gathered} y=-\frac{8}{5}x+\frac{72}{5}-6 \\ \\ y=-\frac{8}{5}x+\frac{42}{5} \end{gathered}[/tex]
And that's the slope-intercept form of the equation.
