Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have
[tex](-6,\ 3)\to x_1=-6,\ y_1=3,\ m=\dfrac{5}{2}[/tex]
Substitute:
[tex]y-3=\dfrac{5}{2}(x-(-6))\\\\y-3=\dfrac{5}{2}(x+6)[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]y-3=\dfrac{5}{2}(x+6)[/tex] use the distributive property
[tex]y-3=\dfrac{5}{2}x+\dfrac{5}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3[/tex]
[tex]y-3=\dfrac{5}{2}x+15[/tex] add 3 to both sides
[tex]y=\dfrac{5}{2}x+18[/tex]
Convert to the standard form:
[tex]Ax+By=C[/tex]
[tex]y=\dfrac{5}{2}x+18[/tex] multiply both sides by 2
[tex]2y=5x+36[/tex] subtract 5x from both sides
[tex]-5x+2y=36[/tex] change the signs
[tex]5x-2y=-36[/tex]
