Find the Slope and Y-Intercept (2,23) , (6,18)

Math
(2,23) , (6,18)
Find the value of the slope.
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Slope is equal to the change in y over the change in x, or rise over run.
m=change in ychange in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2-y1x2-x1
Substitute in the values of x and y into the equation to find the slope.
m=18-(23)6-(2)
Simplify.
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Simplify the numerator.
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Multiply -1 by 23.
m=18-236-(2)
Subtract 23 from 18.
m=-56-(2)
m=-56-(2)
Simplify the denominator.
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Multiply -1 by 2.
m=-56-2
Subtract 2 from 6.
m=-54
m=-54
Move the negative in front of the fraction.
m=-54
m=-54
m=-54
Find the value of the y-intercept.
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Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-54)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-54)⋅(2)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
23=(-54)⋅(2)+b
Rewrite the equation as (-54)⋅(2)+b=23.
(-54)⋅(2)+b=23
Simplify each term.
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Cancel the common factor of 2.
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Move the leading negative in -54 into the numerator.
-54⋅2+b=23
Factor 2 out of 4.
-52(2)⋅2+b=23
Cancel the common factor.
-52⋅2⋅2+b=23
Rewrite the expression.
-52+b=23
-52+b=23
Move the negative in front of the fraction.
-52+b=23
-52+b=23
Move all terms not containing b to the right side of the equation.
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Add 52 to both sides of the equation.
b=23+52
To write 23 as a fraction with a common denominator, multiply by 22.
b=23⋅22+52
Combine 23 and 22.
b=23⋅22+52
Combine the numerators over the common denominator.
b=23⋅2+52
Simplify the numerator.
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Multiply 23 by 2.
b=46+52
Add 46 and 5.
b=512
b=512
b=512
b=512
The values of the slope and y-intercept are m=-54 and b=512.
m=-54
b=512
Find the Slope and Y-Intercept (2,23) , (6,18)

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