> [!summary] The point slope form equation of a line is a type of equation using the knowledge of one known point and a random point to form the equation of the line. > **Key equation:** > Point-slope form: $y_{2}-y_{1} = m(x_{2} -x_{1})$ >[!info]+ Read Time **⏱ 1 min** # Definition The point slope form equation of a line is a type of line equation that only uses the knowledge of one point and slope to create an equation of a line. ![[slf_1.png|400]] > [!note] Explanation A line with two points and slope labelled. > [!warning] Assumptions Recall that the [[Rate of Change|rate of change]] of a line is the change in the y-direction over the change in x-direction. Assume we know the point $(x_{1},y_{1})$ & the slope $m$ but we dont know the second point $(x_{2},y_{2})$ So, using the information from the image above, the slope would be: $ m = \frac{y_{2}-y_{1}}{x_{2} -x_{1}} $ To create it in the form we want, we rearrange this equation: $ \begin{array}{c} m(x_{2} -x_{1}) = \frac{y_{2}-y_{1}}{\cancel{x_{2} -x_{1}}} (\cancel{x_{2} -x_{1}}) \\ \\ m(x_{2} -x_{1}) = y_{2}-y_{1} \\ \\ \text{We like this equation with change in y on the left} \\ \\ y_{2}-y_{1} = m(x_{2} -x_{1}) \end{array} $ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/Fzb7AdTApf4?si=i3dSfhvk0osg0tsW" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- <!-- Light Mode Newsletter Embed --> <div class="mm-form-light"> <iframe src="https://updates.cyberleadhub.com/widget/form/Y0kpQVpjJQuxEfX59m17" id="inline-Y0kpQVpjJQuxEfX59m17" title="Join Math & Matter Newsletter (Light)" data-height="900" scrolling="no" allowtransparency="true" loading="lazy" style="width:100%;height:350px;border:none;border-radius:10px;background:transparent;overflow:hidden" ></iframe> </div> <!-- Dark Mode Newsletter Embed --> <div class="mm-form-dark"> <iframe src="https://updates.cyberleadhub.com/widget/form/lbeDLm24VjuaFxhjccA1" id="inline-lbeDLm24VjuaFxhjccA1" title="Join Math & Matter Newsletter (Dark)" data-height="900" scrolling="no" allowtransparency="true" loading="lazy" style="width:100%;height:350px;border:none;border-radius:10px;background:transparent;overflow:hidden" ></iframe> </div> <!-- Provider script (only once) --> <script src="https://updates.cyberleadhub.com/js/form_embed.js"></script>