Question

Identify the slope and y-intercept of each line.

$7x-3y=9$.

Short answer

Slope of the line is $\frac{7}{3}$and y-intercept is$\left(0,-3\right)$.

Step-by-step solution

Step 1. Given information

Given equation of the line is$7x-3y=9$.

Step 2. Finding the slope and y-intercept.

Solving the given equation for y, we get

$$\begin{gathered} \Rightarrow 3y=7x-9 \\ \Rightarrow y=\frac{7x-9}{3} \\ \Rightarrow y=\frac{7x}{3}-\frac{9}{3} \\ \Rightarrow y=\frac{7}{3}x-3 \end{gathered}$$

Now comparing with slope-intercept form of the line $y=mx+b$, we get

$m=\frac{7}{3}$and $b=-3$.

Therefore slope of the line is$\frac{7}{3}$and y-intercept is$\left(0,-3\right)$.