Exercise 28 Page 312

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 will use the two given points to calculate these values. Let's find the slope m by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,3) & ( 2,5)

m=5- 3/2- 0

SubTerms

Subtract terms

m=2/2

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= 1x + b ⇔ y=x+ b To complete the equation, we also need to determine the y-intercept b. We can see that one of our given points, (0, 3), lies on the y-axis. Since the line crosses the y-axis at this point, the y-intercept is 3. We can now complete the equation. y=x+ 3