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Exercises Equations and inequalities

Example 11 from Algebra and Trigonometry, 2.2 Linear Equations in One Variable

Finding the Equation of a Line Passing Through Two Given Points

Find the equation of the line passing through the points $(3, 4)$ and $(0, −3) .$ Write the final equation in slope-intercept form.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, we calculate the slope using the slope formula and two points.

$\begin{matrix} y - 4 & = & \frac{7}{3} (x - 3) \\ y - 4 & = & \frac{7}{3} x - 7 Distribute the \frac{7}{3} . \\ y & = & \frac{7}{3} x - 3 \end{matrix}$
Next, we use the point-slope formula with the slope of $\frac{7}{3},$ and either point. Let’s pick the point $(3, 4)$ for $y = \frac{7}{3} x - 3.$

$\begin{matrix} y - 4 & = & \frac{7}{3} (x - 3) \\ y - 4 & = & \frac{7}{3} x - 7 Distribute the \frac{7}{3} . \\ y & = & \frac{7}{3} x - 3 \end{matrix}$

In slope-intercept form, the equation is written as $y = \frac{7}{3} x - 3.$

How did it go?

PreviousFinding the Equation of a Line Given the Slope and One Point Next Finding the Equation of a Line and Writing It in Standard Form

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.