Question

Find an equation for the line that passes through the points (-1,-5) and (-5,1)

Answer 1

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

$y = -\frac{3}{2} x-\frac{13}{2}$

Step-by-step explanation:

1) First, find the slope 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:

$m = \frac{(1)-(-5)}{(-5)-(-1)} \\m = \frac{1+5}{-5+1} \\m = \frac{6}{-4}\\m =- \frac{3}{2}$

2) Next, use the point-slope formula $y-y_1= m (x-x_1)$ to write an equation. Substitute $m$, $x_1$, and $y_1$ for real values.

$m$ represents the slope, so substitute $-\frac{3}{2}$ for it. The $x_1$ and $y_1$ represent the x and y values of one of the points the line intersects, so choose any of the given points and substitute their x and y values into the formula. (Any choice is fine, it will result to the same equation. I chose (-5, 1) as shown below). Finally, isolate y to put the equation into slope-intercept form:

$y-1 = -\frac{3}{2} (x-(-5))\\y-1 = -\frac{3}{2} (x + 5)\\y - 1 = -\frac{3}{2}x - \frac{15}{2} \\y = -\frac{3}{2} x-\frac{15}{2} +\frac{2}{2} \\y = -\frac{3}{2}x - \frac{13}{2}$