Q50. - Algebra 2

Question

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

$g\left(x\right)=0.5x-3$ 

Step-by-Step Solution

Answer

The x-intercept of the given equation is $6$ and the y-intercept is $-3.$

Step 1- Given information

A linear equation $g\left(x\right)=0.5x-3$.

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

$\begin{array}{l}g\left(x\right)=0.5x-3\\ \Rightarrow g\left(x\right)=y=0.5x-3\\ \Rightarrow y=0.5x-3\left(1\right)\end{array}$

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

$\begin{array}{l}0=0.5x-3\\ \Rightarrow 0.5x=3\\ \Rightarrow x=\frac{3}{0.5}\\ \Rightarrow x=6\end{array}$

Therefore, the x-intercept is $6$ and the coordinate is $\left(6,0\right).$

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

$\begin{array}{l}y=0.5\times 0-3\\ \Rightarrow -3\end{array}$

Therefore, the y-intercept is $-3$ and coordinate is $\left(0,-3\right).$

Step 4- Graph of the of the given equation

The graph of the given function is: