Question

What is the equation of the line with the coordinates (-10,-7) and (-5,-9)

Answer 1

`y = - (2)/(5) x - 11`

Explanation:

`(-10,-7) and (-5,-9) \\ x_(1) = - 10 \\ y_(1) = - 7 \\ x_(2) = - 5 \\ y_(2) = - 9`

`(y - y_(1))/(x -x_(1) ) = (y_(2) -y_(1))/(x_(2) - x_(1) ) \\ (y -( - 7) )/(x - ( - 10)) = ( - 9 - ( - 7))/( - 5 - ( - 10)) \\`

`(y + 7)/(x + 10) = ( - 2)/(5) \\ cross \: multiply \\ 5(y + 7) = - 2(x + 10) \\ 5y + 35 = - 2x - 20`

`collect \: like \: terms \: \\ 5y = - 2x - 20 - 35 \\ 5y = - 2x - 55 \\ ( 5y = - 2x - 55)/( 5) \\`

`y = - (2)/(5) x - 11`

Answer 2

y = − 2/5x − 11

Explanation:

To answer this, we need to put it into y = mx + b form. First, we need to find the slope. The equation for that is:

`m = (-9 - (-7))/(-5 - (-10))`

`m = -(2)/(5)`

We now have the slope. Now, we need to figure out b, or the y-intercept. Using y = mx + b, we substitute the slope and an x value (it doesn't matter whether it's -10 or -5, but let's use -10 for now) and a y value (same thing).

`-7 = (-(2)/(5))(-10) + b`

`b = -11`

All that's left to do is plug it in! Our final answer is:

`y = - (2)/(5)x - 11`