# How do you write an equation for the line in point-slope form: passing through (7,8) with x-intercept = 3?

Mar 21, 2016

The x intercept is just another point (3, 0), so we have enough information to find the slope.

#### Explanation:

The formula for slope is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where m is slope and $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ are points.

$m = \frac{0 - 8}{3 - 7}$

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

$m = 2$

Point slope form is $y - {y}_{1} = m \left(x - {x}_{1}\right)$. Like with slope, which point you choose with which role doesn't matter. Let's pick (3, 0) (normally I pick the simpler point to work with).

Your equation in point-slope form: $y - 0 = 2 \left(x - 3\right)$

$y = 2 x - 6$ is your equation in slope intercept form. This is always of the form $y = m x + b$, and is the most used form for the équations of linear functions.

Practice exercises:

1. Find the equation of a line in slope intercept form that passes through (3, 4) and (-11, 6).

$2.$. A linear function has a y intercept at 5 and an x intercept at -2. Find the equation of the function.