Chapter 3: Q. 134 (page 278)

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

Short Answer

Expert verified

The given lines are parallel.

Step by step solution

Step 1. Given information

The given equations are $3 x - 4 y = - 2$ and $y = \frac{3}{4} x - 3$ .

Step 2. Solve for y.

The second given equation is already in the slope-intercept form, so solve the first equation for $y$ .

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

Step 3. Determine slope and y- intercepts.

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

$m = \frac{3}{4}$

The y-intercept of first and second line is $(0, \frac{1}{2})$ and $(0, - 3)$ respectively.

Step 4. Conclusion

Since both the lines have same slope but distinct values of y-intercepts, they are parallel.

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

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.3x-4y=-2;y=34x-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

Decision Maths

Applied Mathematics

Calculus

Geometry

Probability and Statistics

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.
$3 x - 4 y = - 2$ ; $y = \frac{3}{4} x - 3$