Question

What is an equation of the line that passes through the points (-6, -8)and (-3, -3)? Put your answer in fully reduced form.

Answer 1

The equation of the line that passes through the points (-6, -8)and (-3, -3) is

5 x - 3 y + 6 =0

Explanation:

Step(i):-

Given points are ( -6 ,-8) and ( -3 ,-3)

Slope of the line

`m = (y_(2)-y_(1) )/(x_(2) - x_(1) ) = (-3+8)/(-3+6) = (5)/(3)`

Step(ii):-

Slope -point form

`y-y_(1) =m(x-x_(1) )`

`y-(-8) =(5)/(3) (x-(-6) )`

cross multiplication, we get

3(y +8 ) = 5(x+6)

3 y +24 = 5 x +30

5 x - 3 y +30 -24 =0

5 x - 3 y + 6 =0

Final answer:-

The equation of the line that passes through the points (-6, -8)and (-3, -3) is

5 x - 3 y + 6 =0