Chapter 3: Q. 3.41 (page 270)

Use slopes and y-intercepts to determine if the lines are parallel:
ⓐ $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$
ⓑ $y = - \frac{1}{2} x - 1$ and $x + 2 y = - 2$

Short Answer

Expert verified

ⓐ The given lines are parallel.

ⓑ The given lines are not parallel; They are the same line.

Step by step solution

Step 1. Given Information

Pair of lines:

ⓐ $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$

ⓑ $y = - \frac{1}{2} x - 1$ and $x + 2 y = - 2$

Step 2. Required to find

Use slopes and y-intercepts to determine if the lines are parallel

Step 3. Convert the equations into slope and y-intercept form

If the co-efficient of y is not 1, divide the equations by the co-efficient of y, rearrange the terms to make equation of the form $y = m x + b$ .

the equations become:

ⓐ localid="1645503268542" $y = - \frac{2}{5} x + 1$ and $y = - \frac{2}{5} x - 4$

ⓑ $y = - \frac{1}{2} x - 1$ and $y = - \frac{1}{2} x - 1$

Step 4. Compare the slopes and y-intercepts to determine the parallelism

ⓐ The slopes are same and y-intercepts are different. Therefore, the given lines are parallel.

ⓑ The slopes are same and y-intercepts are same as well. Therefore, the given lines are not parallel; They are the same line.

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Use slopes and y-intercepts to determine if the lines are parallel:
ⓐ $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$
ⓑ $y = - \frac{1}{2} x - 1$ and $x + 2 y = - 2$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Required to find

Step 3. Convert the equations into slope and y-intercept form

Step 4. Compare the slopes and y-intercepts to determine the parallelism

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Use slopes and y-intercepts to determine if the lines are parallel:ⓐ 2x+5y=5and y=-25x-4ⓑ y=-12x-1and x+2y=-2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Required to find

Step 3. Convert the equations into slope and y-intercept form

Step 4. Compare the slopes and y-intercepts to determine the parallelism

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Statistics

Decision Maths

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use slopes and y-intercepts to determine if the lines are parallel:
ⓐ $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$
ⓑ $y = - \frac{1}{2} x - 1$ and $x + 2 y = - 2$