Q42. - Algebra 2

Question

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

$2x+5y-10=0$

Step-by-Step Solution

Answer

The x-intercept of the given equation is $5$ and the y-intercept is $2.$

Step 1- Given information

A linear equation $2x+5y-10=0$.

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,

$\begin{array}{l}2x+5y-10=0\\ \Rightarrow 2x+5y=10......\left(1\right)\end{array}$

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

$\begin{array}{l}2x+5\times 0=10\\ \Rightarrow 2x=10\\ \Rightarrow x=5\end{array}$

Therefore, the x-intercept is $5$ and the coordinate is

$\left(5,0\right).$

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

$\begin{array}{l}2\times 0+5y=10\\ \Rightarrow 5y=10\\ \Rightarrow y=2\end{array}$

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: