Q44. - Algebra 2

Question

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.

$44.y=4x-2$

Step-by-Step Solution

Answer

The x-intercept of the given equation is $\frac{1}{2}$ and the y-intercept is $-2.$

Step 1- Given information

A linear equation $y=4x-2$.

Step 2- Concept used

The y-coordinate of the point at which a graph crosses the y-axis is called the y-intercept.

So, the y-intercept is the value of $y$ when $x=0.$ 

The x-coordinate of the point at which a graph crosses the x-axis is called the x-intercept.

So, the x-intercept is the value of $x$ when $y=0.$

Step 3- To find the x-intercept and y-intercept.

From the given information,

$\begin{array}{l}y=4x-2\\ \Rightarrow 4x-y=2\left(1\right)\end{array}$

Substitute the $y=0$ in the equation (1).

$\begin{array}{l}4x-0=2\\ \Rightarrow 4x=2\\ \Rightarrow x=\frac{1}{2}\end{array}$

Therefore, the x-intercept is $\frac{1}{2}$ and the coordinate is $\left(\frac{1}{2},0\right).$

Now, substitute the $x=0$ in the given equation (1).

$\begin{array}{l}4\times 0-y=2\\ \Rightarrow -y=2\\ \Rightarrow y=-2\end{array}$

Therefore, the y-intercept is $-2$ and coordinate is $\left(0,-2\right).$

Step 4- Graph of the of the given equation

The graph of the given equation is: