Question

What is an equation of the line that passes through the points (0, -7) and (-8, 3)?

Answer 1

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

$y = -\frac{5}{4} x-7$  

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:

$m = \frac{(3)-(-7)}{(-8)-(0)}\\m = \frac{3+7}{-8-0} \\m = \frac{10}{-8} \\m = -\frac{5}{4}$

So, the slope is $-\frac{5}{4}$.

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 the $m$, $x_1$, and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{4}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any one of the given points (either 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 (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

$y-(-7) = -\frac{5}{4} (x-(0))\\y + 7 = -\frac{5}{4} x\\y = -\frac{5}{4} x-7$