Question

Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)

Answer 1

The point slope form:
$y - y_1 = m(x - x_1)$

We need to find the slope. To find the slope we can use the following formula:
$\frac{y_2 - y_1}{x_2 - X_1}$

Use the points (-5, 6) and (0, 1) and plug it into our slope formula and solve:
$\frac{1 - 6}{0 - (-5)}$
$\frac{-5}{5} = -1$

So our slope is -1 which means m = slope = -1 
Now that we have our slope lets create the point slope form

Our point slope form equation is $y - y_1 = m(x - x_1)$ Remember 
m = slope = -1. Also, we are going to use the point (-5,6).

First insert the m = slope = -1 number where m is located
$y - y_1 = -1(x - x_1)$

Next, insert the -5 from (-5,6) where $x_1$ is located and the 6 from (-5,6) where $y_1$ is located.
$y - y_1 = -1(x - x_1)$
$y - 6 = -1(x - (-5))$
Now simplify 
$y - 6 = -1(x - (-5))$
$y - 6 = -1(x +5)$ <-------Answer