Q49. - Algebra 2

Question

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

$f\left(x\right)=4x-1$

Step-by-Step Solution

Answer

The x-intercept of the given equation is $\frac{1}{4}$ and the y-intercept is $-1.$

Step 1- Given information

A linear equation $f\left(x\right)=4x-1$.

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,

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

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

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

Therefore, the x-intercept is $\frac{1}{4}$ and the coordinate is

$\left(\frac{1}{4},0\right).$

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

$\begin{array}{l}y=4\times 0-1\\ \Rightarrow y=-1\end{array}$

Therefore, the y-intercept is $-1$ and coordinate is $\left(0,-1\right).$

Step 4- Graph of the of the given equation

The graph of the given function is: