Question

Determine the standard form of the equation of the line that passes through (-2, 0) and (-8,5)

Answer 1

Answer:

$-5x-6y=10$      ←   in standard form

Step-by-step explanation:

The equation of a line in  standard form  is.

$Ax+By=C$

were

• A is a positive integer and

• B, C are integers

As the equation in  point-slope form

$y-y_1=m\left(x-x_1\right)$

where m is the slope and $\left(x_1,\:y_1\right)$  is a point on the line.  

as

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(-8,\:5\right)$

$m=\frac{5-0}{-8-\left(-2\right)}$

$m=-\frac{5}{6}$

using   $m=-\frac{5}{6}$  and $\left(x_1,\:y_1\right)=\left(-2,\:0\right)$  then

$y-0=-\frac{5}{6}\left(x-\left(-2\right)\right)$

$-\frac{5}{6}\left(x-\left(-2\right)\right)=y-0$

$6\left(-\frac{5}{6}\left(x-\left(-2\right)\right)\right)=6y$

$-5\left(x+2\right)=6y$

$-5x-10=6y$

$-5x-6y=10$      ←   in standard form