What is the slope-intercept form of the line passing through  (-2, -1) and (-1, 7) ?

Dec 17, 2015

$y = 8 x + 15$

Explanation:

The slope-intercept form of a line can be represented by the equation:

$y = m x + b$

Start by finding the slope of the line, which can be calculated with the formula:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

where:
$m =$slope
$\left({x}_{1} , {y}_{1}\right) = \left(- 2 , - 1\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(- 1 , 7\right)$

Substitute your known values into the equation to find the slope:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{7 - \left(- 1\right)}{- 1 - \left(- 2\right)}$

$m = \frac{8}{1}$

$m = 8$

So far, our equation is $y = 8 x + b$. We still need to find $b$, so substitute either point, $\left(- 2 , - 1\right)$ or $\left(- 1 , 7\right)$ into the equation since they are both points on the line, to find $b$. In this case, we will use $\left(- 2 , - 1\right)$:

$y = 8 x + b$

$- 1 = 8 \left(- 2\right) + b$

$- 1 = - 16 + b$

$b = 15$

Substitute the calculated values to obtain the equation:

$y = 8 x + 15$