Question

use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).

Answer 1

The slope of the line is

$\frac{-3-1}{6-3}=\frac{-4}{3}$

Substituting into point-slope form using the point (3,1),

$\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}$

Answer 2

Answer: The equation of the line that passes through (6,- 3) and (3,1) is  y = $\frac{-4x}{3}$ +5.

Step-by-step explanation:

Point-slope formula : (y - y1) = m(x - x1)

y = y coordinate of second point

y1     = y coordinate of first point

m = slope

x = x coordinate of second point

x1     = x coordinate of first point

slope (m) = $\frac{1-(-3)}{3-6}$

          m = $\frac{4}{-3}$ or $\frac{-4}{3}$

now put values in point-slope formula  : (y - 1) = $\frac{-4}{3}$(x - 3)

y - 1 = $\frac{-4x}{3\\}$ + 4

y = $\frac{-4x}{3}$ +5

So the equation of the line that passes through (6,- 3) and (3,1) is y = $\frac{-4x}{3}$+5.

Learn more about point-slope here-https://brainly.com/question/6239919

#SPJ10