Question

Graph each equation.

$y=\frac{1}{2}x+1$

Short answer

The graph of the equation $y=\frac{1}{2}x+1$is:

Step-by-step solution

Step 1. Find the x and y- intercepts of the equation y=12x+1.

To find the $x$-intercept, substitute 0 for$y$ and find the value of $x$.

role="math" localid="1647377924678" $$\begin{gathered} y=\frac{1}{2}x+1 \\ 0=\frac{1}{2}x+1 \\ -1=\frac{1}{2}x \\ -1\times 2=x \\ -2=x \end{gathered}$$

Therefore, the $x$-intercept is $-2$.

As, the $x$-intercept is$-2$ that means the graph of$y=\frac{1}{2}x+1$ will intersect the $x$-axis at $\left(-2,0\right)$.

To find the $y$-intercept, substitute 0 for$x$ and find the value of $y$.

role="math" localid="1647378101473" $$\begin{gathered} y=\frac{1}{2}x+1 \\ y=\frac{1}{2}\left(0\right)+1 \\ y=0+1 \\ y=1 \end{gathered}$$

Therefore, the $y$-intercept is 1.

As, the $y$-intercept is 1 that means the graph of$y=\frac{1}{2}x+1$ will intersect the $y$-axis at $\left(0,1\right)$.

Step 2. Draw the graph of the equation y=12x+1.

Draw the graph of the equation$y=\frac{1}{2}x+1$ by using the information that the graph of the equation$y=\frac{1}{2}x+1$ is a line passing through the points$\left(-2,0\right)$ and $\left(0,1\right)$.

Therefore, the graph of the equation$y=\frac{1}{2}x+1$ is: