Answer (assuming it can be in slope-intercept form):
[tex]y = -12x+28[/tex]
Step-by-step explanation:
1) First, find the slope of the line by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(-8)-(4)}{(3)-(2)} \\m = \frac{-8-4}{3-2}\\m = \frac{-12}{1}\\m = -12[/tex]
So, the slope is -12.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute real values for [tex]m[/tex], [tex]x_1[/tex] and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute -12 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, choose one of the given points (any one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (2,4), as seen below.) Finally, isolate y to put the equation in slope-intercept form to find the following answer:
[tex]y-4 = -12(x-2)\\y-4 = -12x+24\\y = -12x+28[/tex]
