Notes
Linear Equations Standard Form
\(Ax+By=C\)
A, B, and C are simplified whole numbers
A is positive.
Practice Questions
Find the x and y intercepts for each of the following.
\(\small{\textbf{1)}}\) \(2x+4y=8\)
\(\small{\textbf{2)}}\) \(x-5y=10\)
\(\small{\textbf{3)}}\) \(-3x-4y=24\)
Rewrite in slope intercept form to find the slope
\(\small{\textbf{4)}}\) \(3x-4y=12\)
\(\small{\textbf{5)}}\) \(-2x+y=6\)
\(\small{\textbf{6)}}\) \(x+2y=12\)
Use Intercepts to graph the following linear equations.
\(\textbf{7)}\) \( 2x-3y=6 \)
\(\textbf{8)}\) \( 2x+y=3 \)
\(\textbf{9)}\) \(x-2y=-3 \)
See Related Pages\(\)
\(\bullet\text{ Slope Intercept Form}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)
\(\bullet\text{ Point Slope Form}\)
\(\,\,\,\,\,\,\,\,y-y_1=m(x-x_1)\)
\(\bullet\text{Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)
\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \) 
\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)
\(\bullet\text{ Net Change}\)
\(\,\,\,\,\,\,\,\,y_2-y_1\)
\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)
\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)
\(\bullet\text{ Andymath Homepage}\)
In Summary
Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B are not both zero. This is a useful form for linear equations because it allows for easy comparison and manipulation of the constants and variables. We can also qfind the slope and intercepts of the line. The slope is equal to -A/B, and the intercepts can be found by setting x=0 and y=0. This information can be used to graph the line on the coordinate plane.
Linear equations in standard form are typically covered in a high school algebra or geometry class.
Some real world examples of linear equations include calculating the distance traveled by a car moving at a constant speed, the amount of money a person earns as a function of the number of hours they work, the number of units a company sells as a function of the price. Anything with a constant growth rate.
The concept of linear equations in standard form was first developed by the French mathematician René Descartes in the 17th century. He is credited with introducing the use of coordinates to represent points in space, which paved the way for the development of graphing techniques.