[tex]\boxed{3x + 4y - 7 = 0}[/tex]
.
First step, find the slope of the line
[tex]\boxed{\boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }}[/tex]
Where
So
[tex]m = \frac{4 - (-2)}{-3 - 5}[/tex]
[tex]m = \frac{4 + 2}{-8}[/tex]
[tex]m = \frac{6}{-8}[/tex]
[tex]m = - \frac{3}{4}[/tex]
Next step, find the equation
[tex]\boxed{\boxed{y - y_1 = m(x - x_1)}}[/tex]
So
[tex]y - (-2) = -\frac{3}{4}(x - 5)[/tex]
[tex]y + 2 = -\frac{3}{4}(x - 5)[/tex]
[tex]4(y + 2) = -3(x - 5)[/tex]
[tex]4y + 8 = -3x + 15[/tex]
[tex]3x + 4y + 8 - 15 = 0[/tex]
[tex]3x + 4y - 7 = 0[/tex]
.
