Exercise 62 Page 322

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 and b. We will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,-4) & ( -7,3)

m=-4- 3/-2-( -7)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=-4-3/-2+7

AddSubTerms

Add and subtract terms

m=-7/5

MoveNegNumToFrac

Put minus sign in front of fraction

m=-7/5

A slope of - 75 means that for every 5 horizontal steps in the positive direction, we take 7 vertical steps in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= -7/5 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 ( -2, -4).

y=-7/5x+b

SubstituteII

x= - 2, y= -4

-4=-7/5 ( - 2)+b

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Solve for b

MultNegNegOnePar

- a(- b)=a* b

-4=7/5*2+b

MoveRightFacToNum

a/c* b = a* b/c

-4=14/5+b

SubEqn

LHS-14/5=RHS-14/5

-4-14/5=b

NumberToFrac

a = 5* a/5

-20/5-14/5=b

SubFrac

Subtract fractions

-34/5=b

A y-intercept of - 345 means that the line crosses the y-axis at the point (0, - 345). We can now complete the equation. y= -7/5x+( -34/5) ⇔ y=-7/5x-34/5