Question

What equation represents the line that passes through (-6,7) and (-3,6)​

Answer 1

Answer:

$y=-\frac{x}{3} +5$

Step-by-step explanation:

we know the two point:

(-6, 7 )

and (-3, 6)

From the first point:

$x_{1}=-6\\y_{1}=7$

and from the second point:

$x_{2}=-3\\y_{2}=6$

with thie information we can find the slope of the line between the poins:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

substituting the values:

$m=\frac{6-7}{-3-(-6)}\\ \\m=\frac{-1}{-3+6}\\ \\m=\frac{-1}{3}$

and now we use the point slope equation to find the equation of the line:

$y=m(x-x_{1})+y_{1}$

substituting the values:

$y=-\frac{1}{3} (x-(-6))+7\\\\y=-\frac{1}{3} (x+6)+7\\\\y=-\frac{x}{3}-\frac{6}{3} +7\\\\y=-\frac{x}{3}-2 +7\\\\y=-\frac{x}{3}+5$

the solution is:

$y=-\frac{x}{3} +5$

Answer 2

y = ( -1 /3)x + 5

hope this helps!