Exercise 11 Page 208

An equation in slope-intercept form follows a specific format. In this case, we are asked to write our equation in function notation. f(x)= mx+ b For an equation in this form, m is the slope and b is the y-intercept. We have also been given two points in function notation. To write these points as coordinate pairs, remember that the input x is the x-coordinate and the output f(x) is the y-coordinate. f( x)= y &⇔&( x, y) f( 3)= -4 &⇔&( 3, -4) f( 5)= -4 &⇔&( 5, -4) Let's use the given points to calculate m and b. We will start by substituting the points into the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 3,-4) & ( 5,-4)

m=-4-( -4)/5- 3

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=-4+4/5-3

AddSubTerms

Add and subtract terms

m=0/2

CalcQuot

Calculate quotient

m=0

A slope of 0 means that our line will be horizontal. Now that we know the slope, we can write a partial version of the equation. f(x)= 0 x+ b ⇒ f(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 to solve for b. Let's use ( 3, -4).

f(x)=b

SubstituteII

x= 3, f(x)= -4

-4=b

RearrangeEqn

Rearrange equation

b=-4

A y-intercept of -4 means that the line crosses the y-axis at the point (0, -4). We can now complete the equation. f(x)= 0x+( -4) ⇒ f(x)=-4