Question

Graph each equation.

$y=-3x+5$

Short answer

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

Step-by-step solution

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

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

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

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

As, the $x$-intercept is$\frac{5}{3}$ that means the graph of$y=-3x+5$ 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 $y$.

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

Therefore, the $y$-intercept is 5.

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

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

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

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