# What is the slope-intercept form of the line passing through  (5, 1) and  0, -6) ?

Mar 31, 2016

$y = \frac{7}{5} x - 6$

#### Explanation:

Recall that the general formula for a line in slope-intercept form is:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = m x + b \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$y =$y-coordinate
$m =$slope
$x =$x-coordinate
$b =$y-intercept

Determining the Equation of the Line
$1$. Start by determining the slope between the two points using the slope formula. When determining the slope, either $\left(5 , 1\right)$ or $\left(0 , - 6\right)$ can be coordinate $1$ or $2$.

As long as you do the calculations correctly, it doesn't matter which one you choose. In this case, we will let coordinate $1$ be $\left(5 , 1\right)$ and coordinate $2$ be $\left(0 , - 6\right)$.

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

$m = \frac{- 6 - 1}{0 - 5}$

$m = \frac{- 7}{- 5}$

$m = \frac{7}{5}$

$2$. Substitute $m = \frac{7}{5}$ into $y = m x + b$. Choose either coordinate $1$ or $2$ into substitute into the equation. In this case, we will choose coordinate $1$. Then solve for $b$.

$y = \frac{7}{5} x + b$

$1 = \frac{7}{5} \left(5\right) + b$

$1 = 7 + b$

$b = - 6$

$3$. Write out the equation.

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = \frac{7}{5} x - 6 \textcolor{w h i t e}{\frac{a}{a}} |}}}$