Question

Find the slope and y-intercept of the line and draw its graph.

$4x+5y=10$

Short answer

Hence, the slope of the line is $-\frac{4}{5}$ and y-intercept is 2 and the graph is

Step-by-step solution

Step 1. Definition of the slope-intercept form.

Point-intercept is the equation of a straight line in the form$y=mx+b$, where m is the slope and b is y-intercept.

Step 2. Find the slope.

We have$4x+5y=10$

First, convert into slope-intercept form:

Subtract $-4x$from both sides of the equation:

$\begin{array}{l}4x+5y-4x=10-4x\\ 5y=-4x+10\end{array}$

Divide both side by 5:

$\begin{array}{l}\frac{5y}{5}=\frac{-4x+10}{5}\\ y=-\frac{4}{5}x+2\end{array}$

Compare the equation with slope intercept form, we get

$m=-\frac{4}{5}$, y-intercept: 2

Step 3. Draw the graph.

Now, interpret the slope as$\frac{\text{Rise}}{\text{Run}}$ and the then move accordingly to plot another point and draw the line through the two points

$\frac{\text{Rise}}{\text{Run}}=\frac{4}{-5}$