Algebra and Trigonometry, 5th Edition

1.4 Equations of Lines and Modeling

• Determine equations of lines.

• Given the equations of two lines, determine whether their graphs are parallel or perpendicular.

• Model a set of data with a linear function.

Slope–Intercept Equations of Lines

In Section 1.3, we developed the slope–intercept equation $y=mx+b$, or $f(x)=mx+b$. If we know the slope and the y-intercept of a line, we can find an equation of the line using the slope–intercept equation.

Example 1

A line has slope $-\frac{7}{9}$ and y-intercept $(0,16)$. Find an equation of the line.

Solution

We use the slope–intercept equation and substitute $-\frac{7}{9}$ for m and 16 for b:

$$\begin{array}{rcl}y& =& mx+b\\ y& =& -\frac{7}{9}x+16,\text{ or}\\ f(x)& =& -\frac{7}{9}x+16.\end{array}$$

Now Try Exercise 7.

Example 2

A line has slope $-\frac{2}{3}$ and contains the point (−3, 6). Find an equation ...