Question

HELP A line passes through two points with coordinates (6,-8) and (-3,7).

Answer 1

Answer:

3y+5x=6

Step-by-step explanation:

Equation of the Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

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

The line passes through the points (6,-8) and (-3,7), thus:

$\displaystyle y+8=\frac{7+8}{-3-6}(x-6)$

$\displaystyle y+8=\frac{15}{-9}(x-6)$

Simplifying:

$\displaystyle y+8=-\frac{5}{3}(x-6)$

Multiplying by 3:

$3(y+8)=-5(x-6)$

$3y+24=-5x+30$

Moving all the variables to the left side:

3y + 5x = 30 - 24

3y + 5x = 6