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A line $\ell$ is parallel to the line with equation $y=17.2x-340.9\text{,}$ but $\ell$ has $y$ -intercept at $(0,128.2)\text{.}$ What is an equation for $\ell\text{?}$

Solution

Parallel lines have the same slope, and the slope of $y=17.2x-340.9$ is $17.2\text{.}$ So $\ell$ has slope $17.2\text{.}$ We have been given that $\ell$ ’s $y$ -intercept is at $(0,128.2)\text{.}$ So we can use slope-intercept form to write its equation as

$y=17.2x+128.2\text{.}$