5.3: Write a Function in SlopeIntercept Form
What if the linear function
Guidance
Remember that a linear function has the form
For instance, the expression
In this case when you substitute
Example A
Consider the function
Solution:
Each number in parentheses is a value of
Function notation tells you much more than the value of the independent variable. It also indicates a point on the graph. For example, in the above example,
Example B
Write an equation for a line with
Solution:
You know the slope, and you know a point on the graph, (–2, 1). Using the methods presented in this Concept, write the equation for the line.
Begin with slopeintercept form.
Example C
Write an equation for a line with
Solution:
You know two points on the graph. Using the methods presented in the previous Concept, write the equation for the line. First, you must find the slope:
Now use the slopeintercept form:
Video Review
Guided Practice
Write an equation for a line with
Solution:
Notice that the first point given as an input value is 0, and the output is 2, which means the point is (0,2). This is the
Now use the slopeintercept form.
Now we find the values of
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK12 Basic Algebra: Linear Equations in SlopeIntercept Form (14:58)
 Consider the function
f(x)=−2x−3. Findf(−3),f(0), andf(5) .  Consider the function
f(x)=23x+10. Findf(−9),f(0), and \begin{align*}f(9)\end{align*}f(9) .
In 3 – 10, find the equation of the linear function in slope–intercept form.

\begin{align*}m=5, f(0)=3\end{align*}
m=5,f(0)=−3 
\begin{align*}m=2\end{align*}
m=−2 , \begin{align*}f(0)=5\end{align*}f(0)=5 
\begin{align*}m=7, f(2)=1\end{align*}
m=−7,f(2)=−1 
\begin{align*}m=\frac{1}{3}, f(1)=\frac{2}{3}\end{align*}
m=13,f(−1)=23 
\begin{align*}m=4.2, f(3)=7.1\end{align*}
m=4.2,f(−3)=7.1 
\begin{align*}f\left (\frac{1}{4}\right )=\frac{3}{4}, f(0)=\frac{5}{4}\end{align*}
f(14)=34,f(0)=54  \begin{align*}f(1.5)=3, f(1)=2\end{align*}
 \begin{align*}f(1)=1\end{align*}, \begin{align*}f(1)=1\end{align*}
Mixed Review
 Translate into a sentence: \begin{align*}4(j+2)=400\end{align*}.
 Evaluate \begin{align*}0.45 \cdot 0.2524 \div \frac{1}{4}\end{align*}.
 The formula to convert Fahrenheit to Celsius is \begin{align*}C(F)=\frac{F32}{1.8}\end{align*}. What is the Celsius equivalent to \begin{align*}35^\circ F\end{align*}?
 Find the rate of change: The diver dove 120 meters in 3 minutes.
 What percent of 87.4 is 106?
 Find the percent of change: The original price was $25.00. The new price is $40.63.
 Solve for \begin{align*}w: \ 606=0.045(w4000)+0.07w\end{align*}.
Notes/Highlights Having trouble? Report an issue.
Color  Highlighted Text  Notes  

Please Sign In to create your own Highlights / Notes  
Show More 