Exercise 4 Page 186

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 ( - 8.3,- 5.2) & ( 6.4,9.5)

m=9.5-( - 5.2)/6.4-( - 8.3)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=9.5+5.2/6.4+ 8.3

AddTerms

Add terms

m=14.7/14.7

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 ( 6.4, 9.5).

y=x+b

SubstituteII

x= 6.4, y= 9.5

9.5= 6.4+b

▼

Solve for b

SubEqn

LHS-6.4=RHS-6.4

9.5-6.4=6.4+b-6.4

SubTerm

Subtract term

3.1=b

RearrangeEqn

Rearrange equation

b=3.1

A y-intercept of 3.1 means that the line crosses the y-axis at the point (0, 3.1). We can now complete the equation. y= 1x+ 3.1 ⇔ y =x+3.1