Chapter 3: Q. 148 (page 278)

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

Short Answer

Expert verified

Neither parallel nor perpendicular.

Step by step solution

Step 1. Given information

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

Step 2. Solve for y.

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

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

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

Step 3. Determine slopes

Now both equations are in slope-intercept form.
Determine the slopes $m_{1}$ and $m_{2}$ by comparing both equations with $y = m x + b$ .

$\begin{array}{rcl} m_{1} & = & - \frac{1}{2} \\ m_{2} & = & - 2 \end{array}$

The obtained slopes are neither same nor negative reciprocal of each other. So, the given lines are neither parallel nor perpendicular.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for y.

Step 3. Determine slopes

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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=3;6x+3y=2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for y.

Step 3. Determine slopes

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Probability and Statistics

Mechanics Maths

Logic and Functions

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.
$2 x + 4 y = 3$ ; $6 x + 3 y = 2$