Answer:
[tex]y-4=\frac{2}{5}(x+2)[/tex]
[tex]y=\frac{2}{5}x+\frac{24}{5}[/tex]
[tex]2x-5y=-24[/tex]
Step-by-step explanation:
we know that
The equation of a line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
In this problem we have
[tex]m=\frac{2}{5}[/tex]
[tex](-2,4)[/tex]
substitute
[tex]y-4=\frac{2}{5}(x+2)[/tex] ----> equation in point slope form
Convert to slope intercept form
[tex]y=\frac{2}{5}x+\frac{4}{5}+4[/tex]
[tex]y=\frac{2}{5}x+\frac{24}{5}[/tex] ----> equation in slope intercept form
Convert to standard form
[tex]y=\frac{2}{5}x+\frac{24}{5}[/tex]
Multiply by 5 both sides to remove the fraction
[tex]5y=2x+24[/tex]
[tex]2x-5y=-24[/tex] -----> equation i standard form
