Prospect Prep
Slopeintercept form is one of the most common ways to express a linear equation. When plotted on the xy axis, a linear equation creates a straight line.
The best thing about slopeintercept form is that it shows you two vital statistics of the line at a glance: the line's slope, m, and its yintercept at the point (0, b). With this information, you can quickly sketch the line on the xy axis.
Example 1:
Example 2:
Plot Lines Using SlopeIntercept Form
 Mark the yintercept point (0, b).
 Using the slope value, find another point on the line. A positive value for slope indicates a line that goes up from left to right. A negative value indicates a line that goes down from left to right.
 Connect the points and extend the line in both directions.
Practice Problems
Problem A:
This line crosses the yaxis at the point (0, 4) and has a slope of 3.
A slope of 3 means that the line's rise to run ratio is 3:1. In other words, it rises three units for every one unit it runs from left to right.
 Mark the point (0, 4).
 Extrapolate: from the yintercept, go up three and over one, and draw another point at (1, 1).
 Connect the points, and extend the line.
Problem B:
The line crosses the yaxis at (0, 25) and has a slope of 5.
In other words, the line "drops" five units for every one unit it goes right.
 Mark the yintercept (0, 25).
 Extrapolate: from the yintercept, go down five and over one, and mark that point (1, 20).
 Connect the points and extend the line.
Problem C:
The coefficient of x in this one is ½, which means this line drops down one unit for every two it goes right.
 Find the yintercept at (0, 3).
 Extrapolate using the slope of ½. Count one unit down, then two units to the right, and draw a point at (2, 2).
 Connect the points and extend.
How to Put a Linear Equation Into SlopeIntercept Form
Isolating y: To get a linear equation into slopeintercept form, you need to get the y variable all alone on one side of the equal sign. Once you isolate y, the coefficient of x becomes the constant m, the slope, and whatever's left over is b, your yintercept (the point where the line crosses the yaxis).
Example 1:
 To isolate y, you have to subtract 3x from both sides.
Example 2:
 To isolate y, first subtract 2x from both sides.
 Divide both sides by 4.
 Then, simplify the equation.
How to Calculate the Slope of a Line When Given Two Points
Calculate the slope of a line that connects the points (1, 2) and (5, 4).
 The difference in the values of the ycoordinates (the "rise") of the two points is (4  2) = 2.
 The difference in the values of the xcoordinates (the "run") of the two points is (5  1) = 4.
So, slope = rise ÷ run = 2 ÷ 4 = ½.
*When you're calculating slope, it doesn't matter which point you call (x_{1}, y_{1}) and which one you call (x_{2}, y_{2}). You just need to be consistent when plugging in the values into the equation.
Try it!
What are the slopes of the following pairs?
 (2, 3) and (7, 4)
 (3, 2) and (4, 7)
 (5, 2) and (1, 3)
 (3, 5) and (4, 9)
 (1, 1) and (0, 2)
 (4, 9) and (4, 17)
(Answers: 1/5; 5; 1/6; 2; 1; 1)

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