How to Calculate Slope & Intercept
To write the equation of a line, you need two items, which are its slope and any point on that line. With this information and using the point-slope formula, you can solve the linear equation to get the slope- intercept form. The slope is the number that measures the steepness of a line, while the y-intercept of a graph is a point at which the graph will cross the y-axis. Learn to use the point-slope form to calculate the slope and intercept of a linear equation with this tutorial.
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Instructions
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The Steps
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1
Recognize that when you have two points on a line with coordinates A(xA, yA ) and B(xB , yB ), the slope m= (yB - yA )/(xB - xA ). Know also that the point- slope form using the point A(xA , yA ) is given by y- yA = m(x- xA ) which when solved for y becomes the slope-intercept form y=mx+b where b is the y-intercept, which is the equation for a line. Note that the values for point B(xB , yB ) can be used in the point-slope form to find similarly the slope-intercept form.
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2
Calculate slope and the intercept for a line l that passes through the points A (-1, 3) and B (1, 7).
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3
Find the slope by using the equation for slope given in Step 1 as (yB - yA )/(xB - xA ). To get that m= (7-3)/ (1- (-1)) = 4/2=2.
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4
Use the point-slope intercept form given in Step 1 with either of the two given points. Let's use B (1, 7) and substituting these values and the slope "m" into the point-slope form, you get the equation y-7= 2(x-1) =2x-2. Add 7 to both sides of the equation to solve for y. The line equation then becomes y= 2x+5, which is in the slope=intercept form where slope =m=2 and the y-intercept=b=5.
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5
Add 7 to both sides of the equation to solve for y. The equation then becomes y= 2x+5. This is the equation of a line given in the slope-intercept form where slope m=2 and the y-intercept b=5. Note that if you use point A instead of point B in Step 5 and do the calculation for the point-slope form, you still get the same equation for the line as y= 2x+5.
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References
Resources
- Photo Credit Wikimedia Commons,http://commons.wikimedia.org/wiki/File:Slope_picture.svg
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Comments
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stevemar2
Oct 17, 2009
Slope and intercept seem to be tough concepts for students to understand, but I think this is helpful information. I also have written math-related eHow articles, so I enjoyed reading this.
