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

1 Answer
Noah G
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 = (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.

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