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

Question

asked Oct 11, 2020 89.7k views

2 Answers

Srgbnd · Answer 1 · 2020-10-16T21:09:11+0000

Answer:

y=-(x)/(3) +5

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=(y_(2)-y_(1))/(x_(2)-x_(1))

substituting the values:

$m=(6-7)/(-3-(-6))\\ \\m=(-1)/(-3+6)\\ \\m=(-1)/(3)$

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:

$y=-(1)/(3) (x-(-6))+7\\\\y=-(1)/(3) (x+6)+7\\\\y=-(x)/(3)-(6)/(3) +7\\\\y=-(x)/(3)-2 +7\\\\y=-(x)/(3)+5$

the solution is:

y=-(x)/(3) +5