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).I need a short version of this if possible and the slope amount please thank you

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

point 01 (6 , -3)

point 02 (3 , 1)

Step 02:

equation of the line:

slope:

$m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}=\frac{1\text{ - \lparen-3\rparen}}{3\text{ - 6}}=\frac{1+3}{-3}=\frac{4}{-3}=-\frac{4}{3}$

Point-slope form of the line

(y - y1) = m (x - x1)

$\begin{gathered} (y\text{ - \lparen-3\rparen\rparen = -}\frac{4}{3}(x\text{ - 6\rparen} \\ \\ (y\text{ + 3\rparen = }\frac{-4}{3}x\text{ + }\frac{24}{3} \\ \\ (y\text{ + 3\rparen = }\frac{-4}{3}x\text{ + 8} \\ \\ y\text{ = - }\frac{4}{3}x\text{ + 8 - 3} \\ \\ y\text{ = - }\frac{4}{3}x\text{ + 5} \end{gathered}$

The answer is:

y = - 4/3 x + 5