Question

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

Answer 1

Answer:

y = − 2/5x − 11

Step-by-step 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:

$m = \frac{-9 - (-7)}{-5 - (-10)}$

$m = -\frac{2}{5}$

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).

$-7 = (-\frac{2}{5})(-10) + b$

$b = -11$

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

$y = - \frac{2}{5}x - 11$

Answer 2

Answer:

$y = - \frac{2}{5} x - 11$

Step-by-step explanation:

$(-10,-7) and (-5,-9) \\ x_{1} = - 10 \\ y_{1} = - 7 \\ x_{2} = - 5 \\ y_{2} = - 9$

$\frac{y - y_{1}}{x -x_{1} } = \frac{y_{2} -y_{1}}{x_{2} - x_{1} } \\ \frac{y -( - 7) }{x - ( - 10)} = \frac{ - 9 - ( - 7)}{ - 5 - ( - 10)}$

$\frac{y + 7}{x + 10} = \frac{ - 2}{5} \\ cross \: multiply \\ 5(y + 7) = - 2(x + 10) \\ 5y + 35 = - 2x - 20$

$collect \: like \: terms \: \\ 5y = - 2x - 20 - 35 \\ 5y = - 2x - 55 \\ \frac{ 5y = - 2x - 55}{ 5}$

$y = - \frac{2}{5} x - 11$