Chapter 3: Q. 135 (page 278)

In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.
$2 x - 4 y = 6$ ; $x - 2 y = 3$

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

Step 1. Given information

The given equations are $2 x - 4 y = 6$ and $x - 2 y = 3$ .

Step 2. Solve for y.

Solve both the equations to obtain the value of $y$ in terms of $x$ .

$\begin{array}{rcl} 2 x - 4 y & = & 6 \\ - 4 y & = & 6 - 2 x \\ \frac{- 4 y}{- 4} & = & \frac{6 - 2 x}{- 4} \\ y & = & - \frac{3}{2} + \frac{1}{2} x \end{array}$

$\begin{array}{rcl} x - 2 y & = & 3 \\ - 2 y & = & 3 - x \\ \frac{- 2 y}{- 2} & = & \frac{3 - x}{- 2} \\ y & = & - \frac{3}{2} + \frac{1}{2} x \end{array}$

Step 3. Determine slope and y- intercepts.

Now both equations are in slope-intercept form.
Determine the slope by comparing both equations with $y = m x + b$ .

$m = \frac{1}{2}$

The y-intercept of first and second line is $(0, - \frac{3}{2})$ and $(0, - \frac{3}{2})$ respectively.

Step 4. Conclusion

Since both the lines have same slope and same values of y-intercepts, so they are neither parallel nor perpendicular to each other.

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In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.
$2 x - 4 y = 6$ ; $x - 2 y = 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for y.

Step 3. Determine slope and y- intercepts.

Step 4. Conclusion

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In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.2x-4y=6;x-2y=3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for y.

Step 3. Determine slope and y- intercepts.

Step 4. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.
$2 x - 4 y = 6$ ; $x - 2 y = 3$