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:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the points (6,-8) and (-3,7), thus:
[tex]\displaystyle y+8=\frac{7+8}{-3-6}(x-6)[/tex]
[tex]\displaystyle y+8=\frac{15}{-9}(x-6)[/tex]
Simplifying:
[tex]\displaystyle y+8=-\frac{5}{3}(x-6)[/tex]
Multiplying by 3:
[tex]3(y+8)=-5(x-6)[/tex]
[tex]3y+24=-5x+30[/tex]
Moving all the variables to the left side:
3y + 5x = 30 - 24
3y + 5x = 6
