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Big Ideas Math Geometry, 2014 View details

5. Equations of Parallel and Perpendicular Lines

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Exercise 4 Page 155

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 = 3 x + 2

If we write the desired equation in slope-intercept form,

y = m x + b,

we can add this slope.

y = 3 x + 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 = 3 x + b

SubstituteII

$x = 1$ , $y = - 2$

- 2 = 3 (1) + b

▼

Solve for

b

MultByOne

$a \cdot 1 = a$

- 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 = 3 x + 2

that passes through

(1, - 2) .

y = 3 x + (- 5) \Leftrightarrow y = 3 x - 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