Exercise 1 Page 183

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. We can calculate the slope by substituting two points from the given table into the Slope Formula. Let's choose the points (-2,4) and (0,5).

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,4) & ( 0,5)

m=5- 4/0-( -2)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=5-4/0+2

AddSubTerms

Add and subtract terms

m=1/2

A slope of 12 means that for every 2 horizontal steps in the positive direction, we take 1 vertical step in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= 1/2 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 ( 0, 5).

y=1/2x+b

SubstituteII

x= 0, y= 5

5=1/2( 0)+b

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Solve for b

ZeroPropMult

Zero Property of Multiplication

5=0+b

IdPropAdd

Identity Property of Addition

5=b

RearrangeEqn

Rearrange equation

b=5

A y-intercept of 5 means that the line crosses the y-axis at the point (0, 5). We can now complete the equation. y= 1/2x+ 5