Question

Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.y = −2x +1x-intercept: ( ?,0)y-intercept: (0,?)

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function

`y=-2x+1`

STEP 2: Determine the x-intercept for the given function.

To determine the x intercept, we set y equals zero and solve for x. Therefore, we have:

`\begin{gathered} y=-2x+1 \\ y=0 \\ \therefore\Rightarrow0=-2x+1 \\ Collect\text{ like terms,} \\ 0-1=-2x \\ -1=-2x \\ Divide\text{ both sides by -2} \\ -(1)/(-2)=(-2x)/(-2) \\ (1)/(2)=x \\ x=0.5 \\ \\ \therefore x-intercepts\Rightarrow(0.5,0) \end{gathered}`

STEP 3: Get the y-intercept

We can get the y-intercept by setting x towards zero and solve for y

`\begin{gathered} y=-2x+1 \\ x=0 \\ y=-2(0)+1 \\ y=0+1 \\ y=1 \\ \\ \therefore y-intercept\Rightarrow(0,1) \end{gathered}`

STEP 4: Plot the graph of the given function