Question

Which equation represents the line that passes through (–6, 7) and (–3, 6)?

Answer 1

y= -1/3x+5 is the equation to represent this line

Answer 2

Equation of line become
`y= (- 1 *x)/(3)+ 5`.

Explanation:

slope of the line

we know that the formula to calculate the slope between two points is equal to

Slope (m) =
`(y_(2)- y_(1) )/(x_(2)-x_(1))`.

substitute the values

(m) =
`\frac{6 - 7} }{ -3 - (-6)}`.

(m) =
`\frac{-1} }{3}`.

With the slope m and the point (-6, 7) find the equation of the line

we know that

the equation of the line in the point-slope form is equal to

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

substitute the values

`(y - 7) = (-1)/(3) (x - ( -6))`.

`(y - 7) = (-1)/(3) (x + 6)`.

`(y - 7) = (-x)/(3) +2 )`.

On adding both sides by 7.

`y= (-x)/(3)  - 2 + 7`.

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

Therefore, equation of line become
`y= (-1 *x)/(3)+ 5`.