Q5. - Algebra 1

Question

Graph each equation.

$-3x=5-y$

Step-by-Step Solution

Answer

The graph of the equation $-3x=5-y$ is:

Step 1. Find the x and y -intercepts of the equation − 3 x = 5 − y .

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

$$\begin{gathered} -3x=5-y \\ -3x=5-0 \\ -3x=5 \\ x=\frac{5}{-3} \\ x=\frac{-5}{3} \end{gathered}$$

Therefore, the x-intercept is $-\frac{5}{3}$.

As, the x-intercept is $-\frac{5}{3}$ that means the graph of $-3x=5-y$ will intersect the x-axis at $\left(-\frac{5}{3},0\right)$.

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

$$\begin{gathered} -3x=5-y \\ -3\left(0\right)=5-y \\ 0=5-y \\ y=5 \end{gathered}$$

Therefore, the y-intercept is 5.

As, the y-intercept is 5 that means the graph of $-3x=5-y$ will intersect the y-axis at $\left(0,5\right)$.

Step 2. Draw the graph of the equation − 3 x = 5 − y .

Draw the graph of the equation $-3x=5-y$ by using the information that the graph of the equation $-3x=5-y$ is a line passing through the points $\left(-\frac{5}{3},0\right)$ and $\left(0,5\right)$.

 

Therefore, the graph of the equation $-3x=5-y$ is: