Question

what is an equation of the line slope intercept form that lasses through the given point and has a given slope (8,-8) slope :3

Answer 1

It is easier to do this in point-slope form first, then convert to slope-intercept later on. 
Point slope equation is (y-y)=m(x-x), where m is the slope, and the second variables of the parenthesis is the point. 
Now we just input the numbers in. 
y+8=3(x-8)
The 8 is positive for the y because it is backwards for these types of equations. 
And then we can distribute the other side. 
y+8=3x-24
Then we subtract 8 from the y to isolate the y. Add the negatives. 
y=3x-32

Hope I helped!

Answer 2

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 8}}\quad ,&{{ -8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run}\implies 3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-8)=3(x-8)\implies y+8=3x-24 \\\\\\ y=3x-24-8\implies y=3x-32$