Q58. - Algebra 2

Question

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

$-\mathbf{2}\mathbf{x}+\mathbf{5}\mathbf{y}=\mathbf{20}$

Step-by-Step Solution

Answer

The x-intercept of the graph of the given equation is -10 and the y-intercept is 4. The graph of the given equation is given as follows:

Step 1 – State the concept

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

Step 2 – List the given data

The given equation is $-2x+5y=20$.

Step 3 – Find the intercepts

Solving for x-intercept,

 

$-2x+5y=20$  (Given equation)

 

$-2x+5\left(0\right)=20$  (Put $y=0$ in the given equation)

 

$-2x=20$  (Simplify)

 

$\frac{-2x}{-2}=\frac{20}{-2}$  (Divide both sides by -2)

 

$x=-10$   (Simplify)

 

So, the x-intercept is $-10$ and the graph crosses the x-axis at the point $\left(-10,0\right)$.

 

Similarly, solving for y-intercept,

 

$-2x+5y=20$  (Given equation)

 

$-2\left(0\right)+5y=20$  (Put $x=0$ in the given equation)

 

$5y=20$  (Simplify)

 

$\frac{5y}{5}=\frac{20}{5}$  (Divide both sides by 5)

 

$y=4$   (Simplify)

 

So, the y-intercept is $4$and thus the graph crosses the y-axis at the point $\left(0,4\right)$.

Step 4 – Graph the equation

Graphing the given equation using the obtained ordered pairs,