Chapter 4: Q. 4.102 (page 513)

Use slopes and y-intercepts to determine if the lines $4 x - 3 y = 6$ and $y = \frac{4}{3} x - 1$ are parallel.

Short Answer

Expert verified

The lines have the same slope and different y-intercepts and so they are parallel.

Step by step solution

Step 1. Given information.

The given equations are:

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

Step 2. Write the equation in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where m is the slope and $(0, b)$ is the y-intercept.

The first equation can be written as:

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

The second equation is already in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

For the first equation, $m = \frac{4}{3}$ and the y-intercept is $(0, - 2)$ .

For the second equation, $m = \frac{4}{3}$ and the y-intercept is $(0, - 1)$ .

The lines have the same slope and different y-intercepts and so they are parallel.

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Use slopes and y-intercepts to determine if the lines $4 x - 3 y = 6$ and $y = \frac{4}{3} x - 1$ are parallel.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

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Use slopes and y-intercepts to determine if the lines 4x-3y=6and y=43x-1are parallel.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

One App. One Place for Learning.

Most popular questions from this chapter

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Use slopes and y-intercepts to determine if the lines $4 x - 3 y = 6$ and $y = \frac{4}{3} x - 1$ are parallel.