Question

The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y– 3 = {(x - 1). What is the

Answer 1

Answer:

$y=\dfrac{1}{2}x+\dfrac{5}{2}$.

Step-by-step explanation:

If a line passing through two points, then the equation of line is

$(y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

It is given that the passing through (1,3) and (-9,-2).  So, equation of line in point slope form is

$\Rightarrow (y-3)=\dfrac{-2-3}{-9-1}(x-1)$

$\Rightarrow (y-3)=\dfrac{1}{2}(x-1)$

Slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

Now,

$(y-3)=\dfrac{1}{2}(x-1)$

$\Rightarrow (y-3)=\dfrac{1}{2}(x}-\dfrac{1}{2}(1)$

$\Rightarrow y=\dfrac{1}{2}(x}-\dfrac{1}{2}+3$

$\Rightarrow y=\dfrac{1}{2}x+\dfrac{5}{2}$

Therefore, the required equation is $y=\dfrac{1}{2}x+\dfrac{5}{2}$.