Question

(4,-8), (-3, 1) in slope intercept form please and thank you

Answer 1

To find the slope we need to apply:

$\text{slope = m=}\frac{(y_2-y_1)}{(x_2-x_1)}$

We have two points and we have:

$\begin{gathered} (x_1,y_1)=(4,-8) \\ (x_2,y_2)=(-3,1) \\ \end{gathered}$

Now we find m,

$\begin{gathered} \text{m=}\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{(1-(-8))}{(-3-4)}=\frac{1+8}{-7}=\frac{9}{-7}; \\ m=\frac{-9}{7} \end{gathered}$

After that, we apply the general equation of the line:

$\begin{gathered} (y-y_1)=m(x-x_1);_{}_{} \\ we\text{ replace the values for m,} \\ x_1=4 \\ y_1=-8 \\ (y-(-8))=\frac{-9}{7}(x-4); \\ y+8=\frac{-9}{7}x+\frac{36}{7} \\ \\ y=\frac{-9}{7}x+\frac{36}{7}-8 \\ y=\frac{-9}{7}x-\frac{20}{7} \end{gathered}$

and from that, the intercept will be:

$b=-\frac{20}{7}$