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Slope and Y - Intercept
What is slope? In math slope is described as rise over run. Slope is defined from left to right where in real life it can be in any direction. Slope or gradient of a line measures its steepness, incline, or the grade. A higher slope means a steeper line and a lower slope means a gradual rise of a line.
The slope of a line in a plane is generally represented by the letter m. Slope is calculated by dividing the delta rise (ΔY) by delta run (ΔX). Delta Raise is the difference between the two points in y axis. It is calculated by counting the units up or down from 1st point to the 2nd point on y axis. Delta Run is the different in two points in X axis. It is calculated by counting the units right or left from 1st point to the 2nd point on X axis.
The slope formula:
(The delta symbol “Δ” is commonly used to identify difference of change.)
There are three types of slopes that we can generally find. A positive slope will be upward if we go from left to right. A negative slope will be downward if we go from left to right. A zero slope will be a flat line. Below are the pictures of three types of slopes.
Figure 1 Figure 2 Figure 3
Figure 1: Slope is upward as we go from left to right
Figure 2: Slope is flat as we go from left to right
Figure 3: Slope is downward as we go from left to right
Calculating Slope: The Slope Calculator above can be used to calculate slope print and turn in as homework. However, the steps to calculating slope manually are below.
Step 1: Find the delta rise (ΔY) by subtracting Y1 from Y2. If the coordinates are (2, 4), (-2, -3) then the ΔY = -7
ΔY = Y2 - Y1
ΔY = -3 - 4
ΔY = - 7
Step 2: Find the delta run (ΔX) by subtracting X1 from X2. If the coordinates are (2, 4), (-2, -3) then the ΔX = -4
ΔX = X2 - X1
ΔX = - 2 - 2
ΔX = - 4
Step 3: Find the slope (m) by dividing the delta rise (ΔY) by delta run (ΔX). The slope is m = 1.75
m = -7/-4
m = 1.75
Slope Example
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Straight Line equation and y-intercept
Knowing how to represent a straight line in an equation and figuring out Y-intercept is very important when it comes to calculating lines and slope. A common form of straight line equation is y = mx + b where m and b are constants. Again, m here is slope, Y is Y1 and X is X1. Use the Slope Calculator above to calculate slope.
Y-intercept is the point on y axis through which a line passes through. Y-intercept is generally denoted as b. For our example above, y-intercept (b) = 0.5. Below is the calculation for y-intercept. You can also use y-intercept calculator above to calculate b.
From above example,
Slope (m) = 1.75, y = 4, x = 2. Plug all that in below
Y = mx + b
4 = 1.75(2) + b
b = 4-3.5
b = .5
Above graph shows y-intercept at (0, .5).
Other Suggested Calculators
Mean, Median & Mode calculator - Just enter the number seperated by comma and hit calculate.
Pathygorean Theorem - Calculate either C, B, or A. Simply plug in the value and get the answers.
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