Question

Graph each equation.

$y=\frac{1}{3}x-2$

Short answer

The graph of the equation is given below.

Step-by-step solution

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$is the slope of the straight line and $c$is the $y$-intercept of the equation.

Also, when both the intercepts are given, use the intercept form of a straight line given below,

$\frac{x}{a}+\frac{y}{b}=1$, where $a$is the $x$-intercept and b is the $y$-intercept.

Step 2. Convert the equation in the intercept form of a line.

The equation of the line $y=\frac{1}{3}x-2$can be written as

$$\begin{gathered} y=\frac{1}{3}x-2 \\ \frac{1}{3}x-y=2 \\ \frac{x}{6}-\frac{y}{2}=1\left[\text{Divideeachtermbyconstantterm}\right] \\ \frac{x}{6}+\frac{y}{\left(-2\right)}=1 \end{gathered}$$

This form of the equation shows the $x$-and and $y$-intercepts of the line. The line meets the $x$-axis at the point$\left(6,0\right)$ and the $y$-axis at the point $\left(0,-2\right)$.

Join these two points and get the plot of the equation of a line.

Step 3. Plot this equation on the Cartesian plane.

Mark the points $\left(6,0\right)$and $\left(0,-2\right)$on a graph and join the two points to form the required line.