Q4. - Algebra 2

Question

Find the x-intercept and the y-intercept of the graph of $\mathbf{3}\mathbf{x}+\mathbf{5}\mathbf{y}=\mathbf{30}$. Then, graph the equation.

Step-by-Step Solution

Answer

The x-intercept of the graph of the given equation is 10 and the y-intercept is 6. 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 $3x+5y=30$.

Step 3 – Find the intercepts

Solving for x-intercept,

 

$3x+5y=30$  (Given equation)

 

$3x+5\left(0\right)=30$  (Put $y=0$ in the given equation)

 

$3x=30$   (Simplify)

 

$\frac{3x}{3}=\frac{30}{3}$  (Divide both sides by 3)

 

$x=10$   (Simplify)

 

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

 

Similarly, solving for y-intercept,

 

$3x+5y=30$  (Given equation)

 

$3\left(0\right)+5y=30$  (Put $x=0$ in the given equation)

 

$5y=30$   (Simplify)

 

$\frac{5y}{5}=\frac{30}{5}$  (Divide both sides by 5)

 

$y=6$   (Simplify)

 

So, the y-intercept is $6$ and thus the graph crosses the y-axis at the point $\left(0,6\right)$.

Step 4 – Graph the equation

Graphing the given equation using the obtained ordered pairs,