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Q6.

Expert-verified
Found in: Page 205

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# Solve each equation by graphing.$4x+2=0$

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

See the 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.

$y=4x+2\phantom{\rule{0ex}{0ex}}=4\left(0\right)+2\phantom{\rule{0ex}{0ex}}=0+2\phantom{\rule{0ex}{0ex}}=2$

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.

$y=4x+2\phantom{\rule{0ex}{0ex}}=4\left(-1\right)+2\phantom{\rule{0ex}{0ex}}=-4+2\phantom{\rule{0ex}{0ex}}=-2$

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 $x=\frac{-1}{2}$.