Exercise 44 Page 190

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) & ( - 5,- 5)

m=- 5-( - 5)/- 5- 0

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=- 5+5/- 5 -0

AddSubTerms

Add and subtract terms

m=0/- 5

0/a=0

m= 0

A slope of 0 means that for every 1 horizontal step in the positive direction, we take 0 vertical steps. 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, - 5), 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+( - 5) → y= - 5