Q16. - Algebra 1

Question

Graph each equation.

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

Step-by-Step Solution

Answer

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

Step 1. Find the x and y - intercepts of the equation y = 1 2 x + 1 .

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

 

$$\begin{gathered} y=\frac{1}{2}x+1 \\ 0=\frac{1}{2}x+1 \\ -1=\frac{1}{2}x \\ -1\times 2=x \\ -2=x \end{gathered}$$

 

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 $y$.

 

$$\begin{gathered} y=\frac{1}{2}x+1 \\ y=\frac{1}{2}\left(0\right)+1 \\ y=0+1 \\ y=1 \end{gathered}$$

 

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 = 1 2 x + 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: