Question

Write the equation of the line that passes through the points (-9, -7) and (-4, 4).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answer 1

Answer:

$y-4 = \frac{11}{5} (x+4)$    

Step-by-step explanation:

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

$m = \frac{(4)-(-7)}{(-4)-(-9)} \\m = \frac{4+7}{-4+9} \\m = \frac{11}{5}$

Thus, the slope is $\frac{11}{5}$.

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

Since $m$ represents the slope, substitute $\frac{11}{5}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, choose any one of the given points (either one is fine, the equation will represent the same line) and substitute its x and y values into the formula as well. (I chose (-4, 4) as seen below.) Make sure to simplify the double negatives to positives. This gives the following answer in point-slope form:  

$y-(4) = \frac{11}{5} (x-(-4))\\y-4 = \frac{11}{5} (x+4)$