Question

Find the equation of a line through the points (2,4) and (3,-8)

Answer 1

Answer (assuming it can be in slope-intercept form):

$y = -12x+28$  

Step-by-step explanation:

1) First, find the slope of the line by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(-8)-(4)}{(3)-(2)} \\m = \frac{-8-4}{3-2}\\m = \frac{-12}{1}\\m = -12$

So, the slope is -12.

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute real values for $m$, $x_1$ and $y_1$.

Since $m$ represents the slope, substitute -12 in its place. Since $x_1$ and $y_1$ 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:

$y-4 = -12(x-2)\\y-4 = -12x+24\\y = -12x+28$