Exercise 76 Page 644

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 ( 3,1) & ( 9,3)

m=3- 1/9- 3

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Evaluate right-hand side

SubTerms

Subtract terms

m=2/6

ReduceFrac

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

m=1/3

Now that we know that the slope is 13, we can write a partial version of the equation. y= 1/3x+ b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points satisfy the equation, we can substitute any of them into the equation to solve for b. Let's arbitrarily use ( 3, 1).

y=1/3x+b

SubstituteII

x= 3, y= 1

1=1/3( 3)+b

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Solve for b

FracMultDenomToNumber

a/3* 3 = a

1=1+b

SubEqn

LHS-1=RHS-1

0=b

RearrangeEqn

Rearrange equation

b=0

A y-intercept of means that the line crosses the y-axis at the point (0, ). We can now complete the equation. y= 1/3x+ ⇔ y=1/3x