Algebra
Lesson 5-4 - Writing Equations in Slope-Intercept Form
Vocabulary: Linear extrapolation is when you use a linear equation to predict values that are beyond the range of the data you are using.
Examples:
Example 1 WRITE AND EQUATION THAT PASSES THROUGH THE POINT (2,7) WITH THE SLOPE OF 3.
Step 1
7=3(2) + b Replace m with 3, y with 7, and x with 2
7=6 + b Simplify
7-6=6 -6 + b minus 6 from both sides
1=b
Step 2
y=3x+1 -- now you have to write the slope- intercept form using m=3 and b=1
Additional Information:
Given the slope and one point
1. Substitute the values of m,x,and y into the slope-intercept from and solve for b.
2. Write the slope intercept form using the values of m and b.
Given two points
1.Find the slope
2.Choose one of the two points to use.
3. Then follow the steps for writing an equations given the slope and one point.
Concept Summary
Given the Slope and One Point
1. Substitute the values of m, x, and y into the slope intercept form and then solve for b.
2. Write the slope intercept form using the values of m and b.
Given Two Points
1. Find the slope.
2. Choose one of the two points to use.
3. Then, follow the steps for writing an equation given the slope and one point. (as seen above)
Given both x and y intercepts
I'll use 6 for the x intercept and -2 for the y intercept for examples.
1. We already have the y intercept so we don't need to worry about that for now. Remember they both are ordered pairs also because the intercept is where the line crosses an axis. So that gives us the points (6,0) and (0,-2)
2. Use the slope equation to find the slope so... -2-0 and that equals -2 or simplified to 1 so there is our slope
0-6 -6 3
3. Put in the information for the equation. y=1/3x-2
I'll do another one for the intercepts of -5 for x and 9 for y.
1.Once again we know that the intercepts are points too so we have the points (-5,0) and (0,9) and also we already have the y intercept so once again we don't need to worry about that.
2. Put in the points into the slope equation. 9-0/0+5(double - make a +) so we get 9/5.
3 Now put in the information and we get y+9/5x+9
OK I'll do one for two given points. I will use (2,8) and (-7,4)
1. Put in the points to the slope equation. 4-8/-7-2
2. Solve for the slope to get -4/-9 and simplify to to get 4/9
3. So now we have the slope but we don't have the y intercept so we have to find it. So pick either of the ordered pairs. I'll use (2,8) because it doesn't have a negative. put in the information into the equation. 8=4/9(2)+b
4. Put the 2 over 1 and multiply the fractions. 4(2)=8 and 9(1)=9
5. We now have 8=8/9+b so multiply both sides by 9 to get rid of the fraction. Now we have 72=8+b
6. Take away 8 from both sides and now we have 64=b
7. Now we have the y intercept so we put it into the equation and get y=4/9x+64
The Equation:
y=mx+b
The Equation:
y=mx+b
Online resources: http://www.sparknotes.com/math/algebra1/writingequations/section1.html
http://www.purplemath.com/modules/strtlneq.htm
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearEqEquationsOfLines.xml
http://www.gomath.com/exercises/SlopeEquationYintercept.php
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearEqEquationsOfLines.xml
http://www.gomath.com/exercises/SlopeEquationYintercept.php
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