Exercise 23 Page 542

Start by using the Slope Formula to find the slope.

Practice makes perfect

An equation in slope-intercept form follows a specific format. y= mx+ b For an equation in this form, m is the slope and b is the y-intercept. Let's use the given points to calculate m. We will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 9,4) & ( 9,6)

m=6- 4/9-( - 9)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=6-4/9+9

AddSubTerms

Add and subtract terms

m = 2/18

ReduceFrac

a/b=.a /2./.b /2.

m= 1/9

A slope of 19 means that for every 9 horizontal steps in the positive direction, we take 1 vertical step in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 1/9 x+ b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 9, 6).

y=1/9x+b

SubstituteII

x= 9, y= 6

6=1/9 * 9+b

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Solve for b

FracMultDenomToNumber

a/9* 9 = a

6 = 1 + b

SubEqn

LHS-1=RHS-1

5 = b