Question

Write an equation and point slope for the line that passes through the giving order pairs there are two correct answers for this question Depending upon which order pair do you use for the slope for

Answer 1

If we label the given points to find the slope of the line, we have:

(4, 1 ) ---> x1 = 4, y1 = 1

(-2, 7) ---> x2 = -2, y2 = 7.

Then, using the formula for the slope of a line, we have:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-1}{-2-4}=\frac{6}{-6}\Rightarrow m=-1$

Then, having this value of m, we can apply the formula for the Point-Slope Form of the line:

1. In the case we take the pair as ( 4, 1), the equation is:

$y-y_1=m(x-x_1)=y-1=-1(x-4)=y-1=-(x-4)$

2. In the case we take the pair as (-2, 7), we have:

$y-7=-1(x-(-2)=y-7=-(x+2)$

Then, we have two options:

$y-1=-(x-4)$$y-7=-(x+2)$