Point-Slope Form
| Site: | Gladwin |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Point-Slope Form |
| Printed by: | Guest user |
| Date: | Wednesday, May 1, 2024, 3:13 AM |
Description
Introduction
Remember that slope is rise/run. The change in y-values between two points on the line represents the rise and the change in the x -values between the same two points determines the run. Therefore the slope of a line given two points on the line can be found by using the following equation:
When the coordinates of a point and the slope of a line are known, the line can be represented in point-slope form. The point-slope formula is 
and is derived from the equation of slope.
This is a formula to find an equation of a line when given a point and the slope.
Example 1
Find the equation of the line that has slope m = 4 and passes through
the point (-1, -6).
Step 1. Identify the slope and point
m = 4, x1 = -1, and y1 = -6.
Step 2. Substitute the values in the Point-Slope Formula and simplify.
y - y1 = m(x - x1)
y - (-6) = (4)(x - (-1))
y + 6 = 4(x + 1)
Example 2
Write the equation of the line in point-slope form that passes through the points (-2, 4) and (1, 2).
Step 1. Identify the points
x1 = -2, x2 = 1; y1 = 4, y2 = 2
Step 2. Substitute the values in the Point-Slope Formula and simplify to find m.
Step 3. Select one point and use m to substitute into formula.
Using (-2, 4) as (x1, y1)
Example 3
Write the equation of the line in point-slope form, given that the slope = -5 and the y-intercept = 4.
Step 1. Substitute the values for slope and the coordinates of the y-intercept into the equation and simplify.
y -intercept (0, 4); m = -5 
and the point (2, 6) is on the line. 
Video Lesson
To learn how to write an equation in point-slope form, select the following link:
Writing Linear Equations in Point-Slope Form
Modeling a Graph
Find the point-slope equation of the line shown in this graph:
Step 1. Identify a point and the slope.
Point: (-1,0)
Slope: 2
Step 2. Substitute the values into the formula.
y - 0 = 2(x + 1)
y = 2(x + 1)
Using Point-Slope Form
To graph an equation written in point-slope form, use the point and slope from the equation to create a line.
Example Graph
Step 1. Identify a point and the slope
Point: (3, 4)
Slope: 
Step 2. Plot (3, 4)
Step 3. Rise 1, run 2 for another point (5, 5)
Step 4. Graph
Video Lesson
To learn how to graph using point slope form, select the following link:
Guided Practices
To solidify your understanding of point slope form, visit the following links. The Hotmath site provides interactive practice with answers available. Click "view solution" to check your work. Click the arrows on the bottom red bar to help with the problem, or use one of the other options below for additional help.
The Holt, Rinehart and Winston Homework Help Online link 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
Graphing Lines Using Point-Slope Form Worksheet
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Answer Key
Graphing Lines Using Point-Slope Form Answer Key
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Sources
Gloag, Anne & Andrew. ""Writing Linear Equations", CK-12 Foundation's Algebra FlexBook." http://www.ck12.org/flexr/flexbook/738/ (accessed December 9, 2009)
Holt, Rinehart, & Winston. "Graphing Lines. "http://my.hrw.com/math06_07/
nsmedia/homework_help/msm3/msm3_ch12_04_homeworkhelp.html (accessed August 13, 2010)
Wilcox, Ted. "Point Slope Form." http://www.freemathhelp.com/point-slope.html(accessed August 13, 2010)