Using the Slope-Intercept Form of an Equation of a Line
Identify the Slope and y-Intercept From an Equation of a Line
In Understand 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 4.41
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.
| \(y=m x+b\) |
|
| Write the equation of the line. | \(y=-3 x+5\) |
| Identify the slope. | \(m=-3\) |
| Identify the y-intercept. | \(\text{y-intercept is 0,5}\) |
Try It 4.81
Identify the slope and y-intercept of the line \(y=\frac{2}{5} x-1\).
Try It 4.82
Identify the slope and y-intercept of the line \(y=-\frac{4}{3} x+1\).
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 4.42
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 \(y\). | \(x +2 y = 6\) |
| Subtract \(x\) from each side. | \(2 y=-x+6\) |
| Divide both sides by 2. | \(\frac{2 y}{2}=\frac{-x+6}{2}\) |
| Simplify. | \(\frac{2 y}{2}=\frac{-x}{2}+\frac{6}{2}\) |
| \(\left(\right.\) Remember: \(\left.\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\right)\) | |
| Simplify. | \(y=-\frac{1}{2} x+3\) |
| Write the slope–intercept form of the equation of the line. | \(y=m x+b\) |
| Write the equation of the line. | \(y=-\frac{1}{2} x+3\) |
| Identify the slope. | \(m=-\frac{1}{2}\) |
| Identify the \(y\)-intercept. | \(\text{y-intercept is 0,3}\) |
Try It 4.83
Identify the slope and y-intercept of the line \(x +4 y = 8 \).
Try It 4.84
Identify the slope and y-intercept of the line \(3 x +2 y = 12 \).