Exercise 18 Page 177

We can find the line that passes through the given points by using the slope-intercept form of an equation. 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 ( - 1,0) & ( 0,0)

m=0- 0/0-( - 1)

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Simplify right-hand side

SubTerm

Subtract term

m=0/0-(- 1)

SubNeg

a-(- b)=a+b

m=0/0+1

AddTerms

Add terms

m=0/1

0/a=0

m=0

A slope of 0 means that the vertical change between any two points is 0. Now that we know the slope, we can write a partial version of the equation. y= 0 x+ b To complete the equation, we also need to substitute the y-intercept, b. We can see that one of our given points, (0, 0), lies on the y-axis. Since the line crosses the y-axis at this point, we know the y-intercept and can complete the equation. y= 0x+ 0 ⇔ y=0