Graphs
| Site: | Gladwin |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Graphs |
| Printed by: | Guest user |
| Date: | Thursday, November 21, 2024, 8:54 AM |
Description
Slope-Intercept Form
A rule for a function can be written by analyzing a graph. Using slope-intercept form, standard form, and point-slope form, functions can be written from a given graph.
To write a function in slope-intercept form given a graph, determine the slope and y-intercept of the graph and then substitute these values into the formula y = mx + b. If it is not possible to determine the y-intercept from the graph, determine a different point, substitute it into the equation and solve for b.
Example Find the function rule for the graph using the slope-intercept form.
Step 1. Choose any two points to find slope. (-3, 1) & (3, -3)
Step 2. Find the value of the y-intercept.
(0, -1)
b = -1
Step 3. Substitute the m and b values into y = mx + b to create the function rule.
Standard Form
To write a function in standard form, follow the same process for writing it in slope-intercept form and then convert the equation to standard form. Remember that the standard form of the equation of a line is 
and when it is converted to slope-intercept form is written as 
.
Example Find the function rule for the graph below and write it in standard form.
Step 1. Choose any two points to find slope. (2, 0) & (0, -4)
Step 2. Find the value of the y-intercept.
(0, -4)
b = -4
Step 3. Substitute the m and b values into y = mx + b to create the function rule.
Step 4. Rewrite the equation in standard form.
Point-Slope Form
To write a function in point-slope form, use any two points to determine the slope. Next, substitute the slope and one of the points into the point-slope formula 
.
Example Find the function rule for the graph using the point-slope form.
Step 1. Choose any two points to find slope. (0, 3) & (1, 1).
Step 2. Pick any point on the line for (x1, y1).
(2, -1)
Step 3. Substitute the values for (x1, y1) and m into y - y1 = m(x - x1) to create the function rule.
y - (-1) = -2(x -2)
Video Lesson
To learn more about writing a function from a graph, select the following link:
Guided Practice
To solidify your understanding of writing a function from a graph & table, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.
Practice
Writing Functions from Graphs Worksheet
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Answer Key
Writing Functions from Graphs Answer Key
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Sources
Algebra.com, "Lesson on Graphing Functions." http://www.algebra.com/algebra/lessons/graphing/ (accessed August 15, 2010)
Stapel, Elizabeth. "Using Slope and y-Intercept to Graph Lines." Purplemath. Available from http://www.purplemath.com/modules/slopgrph.htm. Accessed 11 August 2010
Uploader, Siyavula. "Finding the equation of a straight line graph from a diagram." Connexions. August 12, 2009. http://cnx.org/content/m31271/1.1/.