Answer:
[tex]y=-\frac{x}{3} +5[/tex]
Step-by-step explanation:
we know the two point:
(-6, 7 )
and (-3, 6)
From the first point:
[tex]x_{1}=-6\\y_{1}=7[/tex]
and from the second point:
[tex]x_{2}=-3\\y_{2}=6[/tex]
with thie information we can find the slope of the line between the poins:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
substituting the values:
[tex]m=\frac{6-7}{-3-(-6)}\\ \\m=\frac{-1}{-3+6}\\ \\m=\frac{-1}{3}[/tex]
and now we use the point slope equation to find the equation of the line:
[tex]y=m(x-x_{1})+y_{1}[/tex]
substituting the values:
[tex]y=-\frac{1}{3} (x-(-6))+7\\\\y=-\frac{1}{3} (x+6)+7\\\\y=-\frac{x}{3}-\frac{6}{3} +7\\\\y=-\frac{x}{3}-2 +7\\\\y=-\frac{x}{3}+5[/tex]
the solution is:
[tex]y=-\frac{x}{3} +5[/tex]
