# How do you write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)?

May 16, 2017

The slope-intercept form is $y = \frac{3}{2} x - 1$.

#### Explanation:

First you need to find the slope using the given information.

The equation to use is:

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

where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is one point, and #(x_2,y_2) is the other point.

Let $\left(4 , 5\right)$ be point 1, and $\left(6 , 8\right)$ be point 2.

Substitute the given values into the equation.

$m = \frac{8 - 5}{6 - 4}$

$m = \frac{3}{2}$

Slope intercept form of linear equation:

$y = m x + b$,

where $m$ is the slope and $b$ is the y-intercept.

Use one of the points to determine the y-intercept. I am using $\left(4 , 5\right)$, but $\left(6 , 8\right)$ will give the same answer.

$5 = \frac{3}{2} \times 4 + b$

Simplify.

$5 = \frac{12}{2} + b$

$5 = 6 + b$

Subtract $6$ from both sides.

$- 1 = b$

Slope intercept form of the equation:

$y = \frac{3}{2} x - 1$