Q6. - Algebra 1

Question

Solve each equation by graphing.

$4x+2=0$

Step-by-Step Solution

Answer

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

Step 1. Draw the graph of the equation y = 4 x + 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 4 x + 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 $x=\frac{-1}{2}$.