Question

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

Answer 1

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 = (y_2 - y_1)/(x_2 - x_1)`, where m is slope and `(x_1, y_1) and (x_2, y_2)` are points.

`m = (0 - 8)/(3 - 7)`

`m = -8/-4`

`m = 2`

Point slope form is `y - y_1 = m(x - x_1)`. 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(x - 3)`

`y = 2x - 6` is your equation in slope intercept form. This is always of the form `y = mx + 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.