Lesson
Notes
Problems
\(\textbf{1)}\) Find the equation of the line with slope 3 and goes through the point \((6,4)\).
\(\textbf{2)}\) Find the equation of the line with slope -2 and goes through the point \((-1,5)\).
\(\textbf{3)}\) Find the equation of the line with slope \(\displaystyle\frac{1}{3} \) and goes through the point \((3,8)\).
\(\textbf{4)}\) Find the equation of the line with slope 1 and goes through the point \((-6,-4)\).
\(\textbf{5)}\) Find the equation of the line with slope \(\frac{1}{2}\) and x-intercept \(4\).
\(\textbf{6)}\) Find the equation of the line with slope \(-5\) and y-intercept \(-2\).
See Related Pages\(\)
\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \) 
\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)
\(\bullet\text{ Net Change}\)
\(\,\,\,\,\,\,\,\,y_2-y_1\)
\(\bullet\text{ Slope Intercept Form}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)
\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)
\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)
\(\bullet\text{ Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)
In Summary
Point-slope form \(y – y_1 = m(x – x_1)\) is a common way to express linear equations. It is useful when you know any point \(\left(x_1,y_1\right)\) on the line, and the slope \( m \) of the line. You can easily use the equation to find any other point on the line. Or with a couple steps of algebra you can rewrite the equation in slope intercept form \(y=mx+b\).
Point-slope form is typically covered in a high school algebra or geometry class, but is commonly used in Calculus courses, specifically when finding the equation of a tangent line to a function at a particular point.
Linear equations have a lot of real world examples. Including calculating the distance traveled by a car (or any object) moving at a constant speed, the amount of money a person earns given the number of hours they worked, the income of a company given the number of units they sell at a fixed the price, and many more. Lienar equations will work when modeling anything with a constant growth rate.