Using the Slope-Intercept Form of an 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 \(y=-\frac{4}{3} x+1\).

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 \(3 x +2 y = 12 \).