Exercise 7 Page 187

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 ( 4,19) & ( 9,24)

m=24- 19/9- 4

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Simplify right-hand side

SubTerms

Subtract terms

m=5/5

CalcQuot

Calculate quotient

m=1

A slope of 1 means that for every 1 horizontal step 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 x+ b ⇔ y= 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 ( 4, 19).

y=x+b

SubstituteII

x= 4, y= 19

19= 4+b

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Solve for b

SubEqn

LHS-4=RHS-4

19-4=4+b-4

SubTerm

Subtract term

15=b

RearrangeEqn

Rearrange equation

b=15

A y-intercept of 15 means that the line crosses the y-axis at the point (0, 15). We can now complete the equation. y= 1x+ 15 ⇔ y =x+15