Answer:
3x - 2y = -22
Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y-5=\dfrac{3}{2}(x+4)[/tex] multiply both sides by 2
[tex]2y-(2)(5)=2\!\!\!\!\diagup^1\cdot\dfrac{3}{2\!\!\!\!\diagup_1}(x+4)[/tex]
[tex]2y-10=3(x+4)[/tex] use the distributive property: a(b + c) = ab + ac
[tex]2y-10=(3)(x)+(3)(4)[/tex]
[tex]2y-10=3x+12[/tex] add 10 to both sides
[tex]2y-10+10=3x+12+10[/tex]
[tex]2y=3x+22[/tex] subtract 3x from both sides
[tex]-3x+2y=3x-3x+22[/tex]
[tex]-3x+2y=22[/tex] change the signs
[tex]3x-2y=-22[/tex]
