Which equation represents a line that passes through (–2, 4) and has a slope of 2 Over 5

Accepted Solution

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 thatThe 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 formConvert 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 formConvert 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