Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?
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.
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!
Thank you for visiting. How exciting!