Question

The graph of an equation is shown below.

(a)To find the x-intercept(s) of the graph of an equation, we set$\text{\_\_\_\_}$equal to 0 and solve for$\text{\_\_\_\_}$. So the x-intercept of$2y=x+1$ is$\text{\_\_\_\_}$.

(b)To find the y-intercept(s) of the graph of an equation, we set$\text{\_\_\_\_}$equal to 0 and solve for$\text{\_\_\_\_}$. So the y-intercept of$2y=x+1$ is$\text{\_\_\_\_}$.

Short answer

(a) To find the x-intercept(s) of the graph of an equation, we set y equal to 0 and solve for x. So the x-intercept of $2y=x+1$ is $-1$.

(b) To find the x-intercept(s) of the graph of an equation, we set x equal to 0 and solve for y. So the y-intercept of $2y=x+1$ is $\frac{1}{2}$.

Step-by-step solution

a.Step 1. Apply the concept of intercepts

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Step 2. Compute the x-intercept

Consider the equation $2y=x+1$.

To find the x-intercept, substitute $y=0$ in the equation $2y=x+1$.

Step 3. Calculation step

Replace y by 0 and solve.

$\begin{array}{c}2\left(0\right)=x+1\\ 0=x+1\\ x=-1\end{array}$.

Therefore, x-intercept is $-1$.

Hence, to find the x-intercept(s) of the graph of an equation, we set y equal to 0 and solve for x. So the x-intercept of $2y=x+1$ is $-1$.

b.Step-1 –Apply the concept of intercepts

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Step 2. Compute the y-intercept

Consider the equation $2y=x+1$.

To find the y-intercept, substitute $x=0$ in the equation $2y=x+1$.

Step 3. Calculation step

Replace x by 0 and solve.

$\begin{array}{c}2y=0+1\\ 2y=1\\ y=\frac{1}{2}\end{array}$

Therefore, y-intercept is $\frac{1}{2}$.

Hence, to find the x-intercept(s) of the graph of an equation, we set x equal to 0 and solve for y. So the y-intercept of $2y=x+1$ is $\frac{1}{2}$.