Exercise 46 Page 335

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 ( 0.5,2) & ( 4.5,3)

m=3- 2/4.5- 0.5

SubTerms

Subtract terms

m=1/4

WriteDec

Write as a decimal

m = 0.25

A slope of 0.25 means that for every horizontal step in the positive direction, we take 0.25 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 0.25 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 and solve for b. Let's use ( 0.5, 2).

y=0.25x+b

SubstituteII

x= 0.5, y= 2

2=0.25( 0.5)+b

▼

Solve for b

Multiply

Multiply

2=0.125+b

SubEqn

LHS-0.125=RHS-0.125

2 - 0.125 = 0.125 + b - 0.125

CommutativePropAdd

Commutative Property of Addition

2 - 0.125 = b + 0.125 - 0.125

SubTerms

Subtract terms

1.875 = b

RearrangeEqn

Rearrange equation

b= 1.875

A y-intercept of 1.875 means that the line crosses the y-axis at the point (0,1.875). We can now complete the equation. y= 0.25x+1.875