Q17. - Algebra 1

Question

Graph each equation.

$3x+4y=8$

Step-by-Step Solution

Answer

The graph of the equation $3x+4y=8$ is:

Step 1. Find the x and y - intercepts of the equation 3 x + 4 y = 8 .

To find the $x$-intercept, substitute 0 for $y$ and find the value of $x$.

$$\begin{gathered} 3x+4y=8 \\ 3x+4\left(0\right)=8 \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}$$

 

Therefore, the $x$-intercept is $\frac{8}{3}$.

As, the $x$-intercept is $\frac{8}{3}$ that means the graph of $3x+4y=8$ will intersect the $x$-axis at $\left(\frac{8}{3},0\right)$.

 

To find the $y$-intercept, substitute 0 for $x$ and find the value of $y$.

$$\begin{gathered} 3x+4y=8 \\ 3\left(0\right)+4y=8 \\ 0+4y=8 \\ 4y=8 \\ y=\frac{8}{4} \\ y=2 \end{gathered}$$

 

Therefore, the $y$-intercept is 2.

 

As, the $y$-intercept is 2 that means the graph of $3x+4y=8$ will intersect the $y$-axis at $\left(0,2\right)$.

Step 2. Draw the graph of the equation 3 x + 4 y = 8 .

Draw the graph of the equation $3x+4y=8$ by using the information that the graph of the equation $3x+4y=8$ is a line passing through the points $\left(\frac{8}{3},0\right)$ and $\left(0,2\right)$.

 

Therefore, the graph of the equation $3x+4y=8$ is: