Question

1. A line goes through the points (7, 3) and (–1, 5). Write the equation of the line in point-slope form. Show your work for full credit. (How did you go from those two points to having the equation in point-slope form?)

Answer 1

Answer:

A line goes through the points (7, 3) and (–1, 5).

To find:

The equation of the line in point-slope form.

Solution:

The lines goes through the points (7, 3) and (–1, 5). So, slope of line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{5-3}{-1-7}$

$m=\dfrac{2}{-8}$

$m=-\dfrac{1}{4}$

So, slope of the line is $m=-\dfrac{1}{4}$.

Now,

Point slope  form of a line is

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

where, m is slope and $(x_1,y_1)$ is any point on the line.

If slope of line is $m=-\dfrac{1}{4}$ and the point is (7, 3), then point slope form of line is

$y-3=-\dfrac{1}{4}(x-7)$

If slope of line is $m=-\dfrac{1}{4}$ and the point is (-1, 5), then point slope form of line is

$y-5=-\dfrac{1}{4}(x-(-1))$

Therefore, the required equations are either $y-3=-\dfrac{1}{4}(x-7)$ or  $y-5=-\dfrac{1}{4}(x-(-1))$.