Answer:
[tex]\large\boxed{5x-3y=-46}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have
[tex](-5,\ 7)\to x_1=-5,\ y_1=7\\\\m=\dfrac{5}{3}[/tex]
Substitute:
[tex]y-7=\dfrac{5}{3}(x-(-5))\\\\y-7=\dfrac{5}{3}(x+5)[/tex]
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
Convert
[tex]y-7=\dfrac{5}{3}(x+5)\qquad\text{multiply both sides by 3}\\\\3y-21=5(x+5)\qquad\text{use distributive property}\\\\3y-21=5x+25\qquad\text{subtract 25 from both sides}\\\\3y-46=5x\qquad\text{subtract 3y from both sides}\\\\-46=5x-3y\to5x-3y=-46[/tex]
