Q14. - Algebra 1

Question

Graph each equation.

$y=4x-2$

Step-by-Step Solution

Answer

The graph of the equation $y=4x-2$ is:

Step 1. Find the x and y - intercepts of the equation y = 4 x − 2 .

To find the $x$-intercept, substitute 0 for $y$ and find the value of $x$.

$$\begin{gathered} y=4x-2 \\ 0=4x-2 \\ 2=4x \\ \frac{2}{4}=x \\ \frac{1}{2}=x \end{gathered}$$

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

 

As, the $x$-intercept is $\frac{1}{2}$ that means the graph of $y=4x-2$ will intersect the $x$-axis at $\left(\frac{1}{2},0\right)$.

 

To find the $y$-intercept, 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, the $y$-intercept is $-2$.

 

As, the $y$-intercept is $-2$ that means the graph of $y=4x-2$ will intersect the $y$-axis at $\left(0,-2\right)$.

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

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 $\left(\frac{1}{2},0\right)$ and $\left(0,-2\right)$.

 

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