Answer:
[tex]y=-\frac{5}{7} x+\frac{1}{7}[/tex]
Step-by-step explanation:
Equation of a line: [tex]y = mx+b[/tex]
m is the slope, and b is the y-intercept.
m = [tex]\frac{rise}{run} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{-2-3}{3-(-4)} =-\frac{5}{7}[/tex]
Now, we have [tex]y=-\frac{5}{7} x+b[/tex]
We can insert one set of points in to solve for b.
We will use the first point (-4, 3):
[tex]3=-\frac{5}{7} (-4)+b[/tex]
[tex]\frac{5}{7}* \:4+b=3[/tex]
[tex]\frac{20}{7}+b=3[/tex]
[tex]b=\frac{1}{7}[/tex].
Equation:[tex]y=-\frac{5}{7} x+\frac{1}{7}[/tex]
