Answer:
The equation in point slope form is [tex]y+2=-\frac{4}{7}(x+5)[/tex]
The equation in slope intercept form is [tex]y=-\frac{4}{7}x-\frac{34}{7}[/tex]
The equation in standard form is [tex]4x+7y=-34[/tex]
Step-by-step explanation:
we know that
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{4}{7}[/tex]
[tex]point\ (-5,-2)[/tex]
substitute
[tex]y+2=-\frac{4}{7}(x+5)[/tex] ----> equation of the line in point slope form
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y+2=-\frac{4}{7}x-\frac{20}{7}[/tex]
[tex]y=-\frac{4}{7}x-\frac{20}{7}-2[/tex]
[tex]y=-\frac{4}{7}x-\frac{34}{7}[/tex] ----> slope intercept form
Convert to standard form
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integer
[tex]y=-\frac{4}{7}x-\frac{34}{7}[/tex]
Multiply by 7 both sides to remove the fraction
[tex]7y=-4x-34\\4x+7y=-34[/tex]
