Exercise 10 Page 167

Practice makes perfect

a When lines are parallel, they have the same slope. With this, we know that all lines that are parallel to our given line will have a slope of - 13.

y=-1/3x+4 If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope. y=-1/3x+ b To determine the value of b, we can use the fact that our line must pass through (- 1,- 9). Let's substitute x= - 1 and y= - 9 into the equation and solve for b.

y=-1/3x+b

SubstituteII

x= - 1, y= - 9

- 9=-1/3( - 1)+b

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Solve for b

MultNegNegOnePar

- a(- b)=a* b

- 9=1/3+b

NumberToFrac

a = 3* a/3

-27/3=1/3+b

SubEqn

LHS-1/3=RHS-1/3

-28/3=b

RearrangeEqn

Rearrange equation

b= -28/3

Now that we have the y-intercept, we can conclude the line parallel to y=- 13x+4 that passes through (- 1,- 9). y=-1/3x+( -28/3) ⇔ y=-1/3x-28/3

b When lines are perpendicular, their slopes will be opposite reciprocals of one another. With this, we know that all lines that are perpendicular to our given line will have a slope of 3.

Given Slope:& m_1=- 13 Opposite Reciprocal:& m_2=3 With this information, we can write a general equation for all lines with slope perpendicular to that of the given equation. y=3x+b Once again, to find b, we can substitute x= - 1 and y= - 9 into this equation.

y=3x+b

SubstituteII

x= - 1, y= - 9

- 9=3( - 1)+b

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Solve for b

MultPosNeg

a(- b)=- a * b

- 9=- 3+b

AddEqn

LHS+3=RHS+3

- 6=b