Question

Graph each equation.

$y=2x+3$

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 $y=2x+3$can be written as

role="math" localid="1647412563271" $$\begin{gathered} \frac{-2x}{3}+\frac{y}{3}=\frac{3}{3}\left[\text{Divideeachtermbyconstantterm}\right] \\ \frac{-2}{3}x+\frac{1}{3}y=1 \\ \frac{x}{-3/2}+\frac{y}{3}=1 \\ \frac{x}{-1.5}+\frac{y}{3}=1 \end{gathered}$$

This form of the equation shows the $x$-and and $y$-intercepts of the line. The line meets the $x$-axis at the point $\left(-1.5,0\right)$and the $y$-axis at the point $\left(0,3\right)$.

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$\left(-1.5,0\right)$ and$\left(0,3\right)$ on a graph and join the two points to form the required line.