Exercise 4 Page 155

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 3.

y=3x+2 If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope. y=3x+ b To determine the value of b, we can use the fact that our line must pass through (1,- 2). Let's substitute x= 1 and y= - 2 into the equation and solve for b.

y=3x+b

SubstituteII

x= 1, y= - 2

- 2=3( 1)+b

▼

Solve for b

MultByOne

a * 1=a

- 2=3+b

SubEqn

LHS-3=RHS-3

- 5=b

RearrangeEqn

Rearrange equation

b= - 5

Now that we have the y-intercept, we can conclude the line parallel to y=3x+2 that passes through (1,- 2). y=3x+( -5) ⇔ y=3x-5

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 - 13.

Given Slope:& m_1=3 Opposite Reciprocal:& m_2=- 13 With this information, we can write a general equation for all lines with slope perpendicular to that of the given equation. y=- 1/3x+b Once again, to find b, we can substitute x= 1 and y= - 2 into this equation.

y=- 1/3x+b

SubstituteII

x= 1, y= - 2

- 2=- 1/3( 1)+b

▼

Solve for b

MultByOne

a * 1=a

- 2=- 1/3+b

AddEqn

LHS+1/3=RHS+1/3

1/3-2=b