Identifying the Slope and <em>y</em>-intercept From An Equation of a Line

Identifying the Slope and y-Intercept From an Equation of a Line

In Understanding the Slope of a Line, we graphed a line using the slope and a point. When we are given an equation in slope–intercept form, we can use the y-intercept as the point, and then count out the slope from there. Let’s practice finding the values of the slope and y-intercept from the equation of a line.

Example

Identify the slope and y-intercept of the line with equation \(y=-3x+5\).

Solution

We compare our equation to the slope–intercept form of the equation.

Write the equation of the line.
Identify the slope.
Identify the y-intercept.

When an equation of a line is not given in slope–intercept form, our first step will be to solve the equation for \(y\).

Example

Identify the slope and y-intercept of the line with equation \(x+2y=6\).

Solution

This equation is not in slope–intercept form. In order to compare it to the slope–intercept form we must first solve the equation for\(y\).

Solve for y.	\(x+2y=6\)
Subtract x from each side.
Divide both sides by 2.
Simplify.
\(\left(\text{Remember:}\phantom{\rule{0.2em}{0ex}}\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\right)\)
Simplify.
Write the slope–intercept form of the equation of the line.
Write the equation of the line.
Identify the slope.
Identify the y-intercept.