<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

5.3: Write a Function in Slope-Intercept Form

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Estimated6 minsto complete
%
Progress
Practice Write a Function in Slope-Intercept Form
 
 
 
MEMORY METER
This indicates how strong in your memory this concept is
Practice
Progress
Estimated6 minsto complete
%
Estimated6 minsto complete
%
Practice Now
MEMORY METER
This indicates how strong in your memory this concept is
Turn In

What if the linear function W(g) represented a family's monthly water bill, with g as the number of gallons of water used. If you knew what the function was, could you find W(25)? How about if you knew the slope of the function and the value of W(25)? Could you determine what the function was? Suppose you knew the values of W(25) and W(50). Could you determine the function in this case? After completing this Concept, you'll be able to perform tasks like these.

Guidance

Remember that a linear function has the form f(x)=mx+b. Here f(x) represents the y values of the equation or the graph. So y=f(x) and they are often used interchangeably. Using the functional notation in an equation often provides you with more information.

For instance, the expression f(x)=mx+b shows clearly that x is the independent variable because you substitute values of x into the function and perform a series of operations on the value of x in order to calculate the values of the dependent variable, y.

In this case when you substitute x into the function, the function tells you to multiply it by m and then add b to the result. This process generates all the values of y you need.

Example A

Consider the function f(x)=3x4. Find f(2),f(0), and f(1).

Solution:

Each number in parentheses is a value of x that you need to substitute into the equation of the function.

f(2)=2;f(0)=4; and f(1)=7

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, f(1)=7. This means the ordered pair (–1, –7) is a solution to f(x)=3x4 and appears on the graphed line. You can use this information to write an equation for a function.

Example B

Write an equation for a line with m=3.5 and f(2)=1.

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 slope-intercept form.

Substitute the value for the slope.Use the ordered pair to solve for b.Rewrite the equation.oryy1byf(x)=mx+b=3.5x+b=3.5(2)+b=8=3.5x+8=3.5x+8

Example C

Write an equation for a line with f(1)=2 and f(5)=20.

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:

m=y2y1x2x1=2025(1)=186=3.

Now use the slope-intercept form:

Substitute the value for the slope.Use the ordered pair to solve for b.Rewrite the equation.oryy2byf(x)=mx+b=3x+b=3(1)+b=5=3x+5=3x+5

Video Review

Guided Practice

Write an equation for a line with f(0)=2 and f(3)=4 and use it to find f(5),f(2),f(0), and f(z).

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 y-intercept. So, all we have to do is find the slope and then plug both values into the slope-intercept form:

m=y2y1x2x1=4230=63=2.

Now use the slope-intercept form.

Substitute the value for the slope.Substitute the value for the y-interceptoryyyf(x)=mx+b=2x+b=2x+2=2x+2

Now we find the values of f(5),f(2),f(0), and f(z) for f(x)=2x+2.

f(5)=2(5)+2=10+2=12

f(2)=2(2)+2=2

f(0)=2(0)+2=0

f(z)=2z+2

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. CK-12 Basic Algebra: Linear Equations in Slope-Intercept Form (14:58)

  1. Consider the function f(x)=2x3. Find f(3),f(0), and f(5).
  2. Consider the function f(x)=23x+10. Find f(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.

  1. \begin{align*}m=5, f(0)=-3\end{align*}m=5,f(0)=3
  2. \begin{align*}m=-2\end{align*}m=2, \begin{align*}f(0)=5\end{align*}f(0)=5
  3. \begin{align*}m=-7, f(2)=-1\end{align*}m=7,f(2)=1
  4. \begin{align*}m=\frac{1}{3}, f(-1)=\frac{2}{3}\end{align*}m=13,f(1)=23
  5. \begin{align*}m=4.2, f(-3)=7.1\end{align*}m=4.2,f(3)=7.1
  6. \begin{align*}f\left (\frac{1}{4}\right )=\frac{3}{4}, f(0)=\frac{5}{4}\end{align*}f(14)=34,f(0)=54
  7. \begin{align*}f(1.5)=-3, f(-1)=2\end{align*}
  8. \begin{align*}f(-1)=1\end{align*}, \begin{align*}f(1)=-1\end{align*}

Mixed Review

  1. Translate into a sentence: \begin{align*}4(j+2)=400\end{align*}.
  2. Evaluate \begin{align*}0.45 \cdot 0.25-24 \div \frac{1}{4}\end{align*}.
  3. The formula to convert Fahrenheit to Celsius is \begin{align*}C(F)=\frac{F-32}{1.8}\end{align*}. What is the Celsius equivalent to \begin{align*}35^\circ F\end{align*}?
  4. Find the rate of change: The diver dove 120 meters in 3 minutes.
  5. What percent of 87.4 is 106?
  6. Find the percent of change: The original price was $25.00. The new price is $40.63.
  7. Solve for \begin{align*}w: \ 606=0.045(w-4000)+0.07w\end{align*}.

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Vocabulary

undefined slope

An undefined slope cannot be computed. Vertical lines have undefined slopes.

Image Attributions

Show Hide Details
Description
Difficulty Level:
At Grade
Grades:
8 , 9
Date Created:
Feb 24, 2012
Last Modified:
Nov 14, 2016
Files can only be attached to the latest version of Modality
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.483.L.1
Here