Question

Solve each equation by graphing.

$4x+2=0$

Short answer

The solution of the equation $4x+2=0$is $x=\frac{-1}{2}$.

Step-by-step solution

Step 1. Draw the graph of the equation y=4x+2.

Substitute 0 for x and find the value of y.

$$\begin{gathered} y=4x+2 \\ =4\left(0\right)+2 \\ =0+2 \\ =2 \end{gathered}$$

Therefore, one of the point that satisfies the equation$y=4x+2$ is$\left(0,2\right)$

Substitute$-1$ for x and find the value of y.

$$\begin{gathered} y=4x+2 \\ =4\left(-1\right)+2 \\ =-4+2 \\ =-2 \end{gathered}$$

Therefore, the other point that satisfies the equation$y=4x+2$ is$\left(-1,-2\right)$

Draw the graph of the equation $y=4x+2$by using the information that the graph of the equation $y=4x+2$is a line passing through the points$\left(0,2\right)$ and $\left(-1,-2\right)$.

Therefore, the graph of the equation $y=4x+2$is:

Step 2. Solve the given equation 4x+2=0.

The solution of the equation$4x+2=0$ by graphing can be obtained by finding the value of x where the graph of$y=4x+2$ intersects the x-axis.

From the graph of $y=4x+2$, it can be noticed that the graph of$y=4x+2$ intersects the x-axis at the point $\left(\frac{-1}{2},0\right)$.

Therefore, the solution of the given equation$y=4x+2$ is $x=\frac{-1}{2}$.