Answer :
To answer this question, we can use the two-point equation of the line as follows:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Now, we need to identify the points in order to apply the previous formula:
(3, -2) ---> x1 = 3, y1 = -2
(4, 6) ---> x2 = 4, y2 = 6
Then, we have:
[tex]y-(-2)=\frac{6-(-2)}{4-3}(x-3)[/tex][tex]y+2=\frac{6+2}{4-3}(x-3)=y+2=\frac{8}{1}(x-3)[/tex][tex]y+2=8(x-3)=8x-24[/tex]We applied the distributive property on the right side of the equation.
Finally, we have:
[tex]y+2=8x-24\Rightarrow y=8x-24-2\Rightarrow y=8x-26[/tex]Therefore, the line equation in the slope-intercept form is:
[tex]y=8x-26[/tex]