Model Comparison: Linear Equations & Inequalities

Calculating Slope

If you are given two points $(x<em>1, y</em>1)$ and $(x<em>2, y</em>2)$, the slope $m$ is calculated as:

$m = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$

Parallel and Perpendicular Lines

• Parallel Lines: Have the same slope ($m<em>1 = m</em>2$).

• Perpendicular Lines: Have slopes that are negative reciprocals ($m<em>1 = -\frac{1}{m</em>2}$). For example, if one slope is $\frac{2}{3}$, the perpendicular slope is $-\frac{3}{2}$.

}{3}$</p><h5 id="46c06e75-1c3f-42a5-9966-be164ce76d20" data-toc-id="46c06e75-1c3f-42a5-9966-be164ce76d20" collapsed="false" seolevelmigrated="true">Quick Coefficients Check</h5><p>For a system in the form:<br>$a1x + b1y = c1$$a2x + b2y = c2$</p><ul><li><p><strong>No Solution</strong>:$\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}$</p></li><li><p><strong>Infinite Solutions</strong>:$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$$