4.5 Use the slope–intercept form of an equation of a line  (Page 4/12)

Solution

1. ⓐ $y=\mathrm{-6}$
   This equation has only one variable, $y$ . Its graph is a horizontal line crossing the y -axis at $\mathrm{-6}$ .
2. ⓑ $5x-3y=15$
   This equation is of the form $Ax+By=C$ . The easiest way to graph it will be to find the intercepts and one more point.
3. ⓒ $x=7$
   There is only one variable, $x$ . The graph is a vertical line crossing the x -axis at 7.
4. ⓓ $y=\frac{2}{5}x-1$
   Since this equation is in $y=mx+b$ form, it will be easiest to graph this line by using the slope and y -intercept.

Solution

ⓐ
$\begin{array}{cccccc}\text{Find the Fahrenheit temperature for a Celsius temperature of 0.}\hfill & & & & & F=\frac{9}{5}C+32\hfill \\ \text{Find}F\text{when}C=0.\hfill & & & & & F=\frac{9}{5}\left(0\right)+32\hfill \\ \text{Simplify.}\hfill & & & & & F=32\hfill \end{array}$

ⓑ
$\begin{array}{cccccc}\text{Find the Fahrenheit temperature for a Celsius temperature of 20.}\hfill & & & & & F=\frac{9}{5}C+32\hfill \\ \text{Find}F\text{when}C=20.\hfill & & & & & F=\frac{9}{5}\left(20\right)+32\hfill \\ \text{Simplify.}\hfill & & & & & F=36+32\hfill \\ \text{Simplify.}\hfill & & & & & F=68\hfill \end{array}$

ⓒ Interpret the slope and F -intercept of the equation.

Even though this equation uses $F$ and $C$ , it is still in slope–intercept form.

The slope, $\frac{9}{5}$ , means that the temperature Fahrenheit ( F ) increases 9 degrees when the temperature Celsius ( C ) increases 5 degrees.

The F -intercept means that when the temperature is $0\text{°}$ on the Celsius scale, it is $32\text{°}$ on the Fahrenheit scale.

ⓓ Graph the equation.

We’ll need to use a larger scale than our usual. Start at the F -intercept $\left(0,32\right)$ then count out the rise of 9 and the run of 5 to get a second point. See [link] .