Question

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

$39.5x+3y=15$

Short answer

The x-intercept of the given equation is 3 and the y-intercept is 5.

Step-by-step solution

Step 1- Given information

A linear equation $5x+3y=15$.

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,

$5x+3y=15\left(1\right)$

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

$\begin{array}{l}5x+3\times 0=15\\ \Rightarrow 5x=15\\ \Rightarrow x=3\end{array}$

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

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

$\begin{array}{l}5\times 0+3y=15\\ \Rightarrow 3y=15\\ \Rightarrow y=5\end{array}$

Step 4- Graph of the of the given equation

The graph of the given equation is: