Question

Identify the slope and y-intercept of each line.

$5x-2y=6$.

Short answer

Slope of the line is$\frac{5}{2}$and y-intercept is$\left(0,-3\right)$.

Step-by-step solution

Step 1. Given information

Given equation of the line is$5x-2y=6$.

Step 2. Finding the slope and y-intercept.

Solving the given equation for y, we get

$$\begin{gathered} \Rightarrow 2y=5x-6 \\ \Rightarrow y=\frac{5x-6}{2} \\ \Rightarrow y=\frac{5x}{2}-\frac{6}{2} \\ \Rightarrow y=\frac{5}{2}x-3 \end{gathered}$$

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

$m=\frac{5}{2}$and $b=-3$.

Therefore slope of the line is$\frac{5}{2}$and y-intercept is$\left(0,-3\right)$.