The slope ($m$) defines the steepness of the incline of a linear equation when graphed out.

- Can be described as “rise over run”.
- For consistency, consider a line as it we move from left to right.
- The numerator of m is the rise of the incline (when negative, it goes downward).
- The denominator of m is the run of the incline (rightward movement.
- For example: $m=-{\displaystyle \frac{2}{3}}$, getting from one point to another requires a vertical descent of 2 down and horizontal run of 3 to the right.

Example:

$y=2x+1$

- Determine the slope (m) and y-intercept from the equation (b).
#### y-intercept

$b=1$

$y-int:0.1$

#### slope

$m={\displaystyle \frac{2}{1}}$

$\to {\textstyle \phantom{\rule{0.278em}{0ex}}}rise{\textstyle \phantom{\rule{0.278em}{0ex}}}of{\textstyle \phantom{\rule{0.278em}{0ex}}}2,{\textstyle \phantom{\rule{0.278em}{0ex}}}run{\textstyle \phantom{\rule{0.278em}{0ex}}}of{\textstyle \phantom{\rule{0.278em}{0ex}}}1$

$\to {\textstyle \phantom{\rule{0.278em}{0ex}}}+2{\textstyle \phantom{\rule{0.278em}{0ex}}}to{\textstyle \phantom{\rule{0.278em}{0ex}}}y,{\textstyle \phantom{\rule{0.278em}{0ex}}}+1{\textstyle \phantom{\rule{0.278em}{0ex}}}to{\textstyle \phantom{\rule{0.278em}{0ex}}}x$

- Locate the next coordinate point over to the right from the y-intercept using the slope and plot both on the Cartesian plane.
$0,1\to 0+1,{\textstyle \phantom{\rule{0.278em}{0ex}}}1+2\to (1,3)$

- Connect the dots and extend the line.

- Last Updated: Oct 20, 2023 1:48 PM
- URL: https://sheridancollege.libguides.com/math-skills-hub/linear-equations-and-linear-systems
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