Exercise 6 Page 157

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 ( 1,5) & ( 4,10)

m=10- 5/4- 1

SubTerms

Subtract terms

m=5/3

A slope of 53 means that for every 3 horizontal steps in the positive direction, we take 5 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 5/3 x+ b To determine the y-intercept b, we can substitute one of the points into the equation and solve for b. Let's use ( 1, 5).

y=5/3x+b

SubstituteII

x= 1, y= 5

5=5/3( 1)+b

▼

Solve for b

MultByOne

a * 1=a

5 = 5/3 + b

SubEqn

LHS-5/3=RHS-5/3

5 - 5/3=b

WriteAsFrac

Write as a fraction

15/3 - 5/3 = b

SubFrac

Subtract fractions

10/3 = b

WriteSumFrac

Write as a sum of fractions

9/3 + 1/3 = b

CalcQuot

Calculate quotient

3 + 1/3 = b

AddTerms

Add terms

3 13 = b

RearrangeEqn

Rearrange equation

b=3 13

A y-intercept of 3 13 means that the line crosses the y-axis at the point (0, 3 13).