Notes
Direct Variation Linear Equations
\(y=mx \)
\(\text{Note: Always passes through the point (0,0)}\)
Practice Questions
Are the following linear equations direct variations?
\(\textbf{1)}\) \( y=3x \)
\(\textbf{2)}\) \( y=\frac{1}{2}x+3 \)
\(\textbf{3)}\) \( y=2x-5 \)
\(\textbf{4)}\) \( y=-2x \)
\(\textbf{5)}\) \( y=x \)
\(\textbf{6)}\) \( y=3 \)
See Related Pages\(\)
\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \) 
\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)
\(\bullet\text{ Net Change}\)
\(\,\,\,\,\,\,\,\,y_2-y_1\)
\(\bullet\text{ Point Slope Form}\)
\(\,\,\,\,\,\,\,\,y-y_1=m(x-x_1)\)
\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)
\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)
\(\bullet\text{ Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)
In Summary
Direct variation is a mathematical relationship between two variables in which one variable is directly proportional to the other. This means that the ratio of the two variables is always constant. In other words, if one variable increases, the other variable also increases by the same factor, and if one variable decreases, the other variable also decreases by the same factor.
Direct variation has the form \(y=mx\) or \(y=kx\). Direct variation is sometimes studied along with inverse variation and joint variation. Inverse variation is in the form \(y=\frac{k}{x}\), and joint variation is in the form \(y=kxz\).
A fun fact about the graphs of direct variations is they always go through the origin of the graph, \((0,0)\).
Related topics to direct variation include inverse variation, joint variation, and combined variation. These topics are typically covered in a high school algebra class.