Exercise 2 Page 311

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 ( - 3, 4) & ( 2, - 1)

m=- 1 - 4/2-( - 3)

SubNeg

a-(- b)=a+b

m=- 1 -4/2+3

AddSubTerms

Add and subtract terms

m=- 5/5

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 negative direction. Now that we know the slope, we can write a partial version of the equation. y = - 1x + 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).

y=- 1 x+b

SubstituteII

x= - 3, y= 4

4 = - 1( - 3) + b

MultNegNegOnePar

- a(- b)=a* b

4 = 3 + b

SubEqn

LHS-3=RHS-3

1 = b

RearrangeEqn

Rearrange equation

b = 1

A y-intercept of 1 means that the line crosses the y-axis at the point (0, 1). We can now complete the equation. y = - 1x+ 1 ⇔ y = - x+ 1