Chapter 4: Q. 4.101 (page 513)

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

$\begin{array}{rcl} 2 x + 5 y & = & 5 \\ y & = & - \frac{2}{5} x - 4 \end{array}$

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:

$\begin{array}{rcl} 5 y & = & - 2 x + 5 \\ y & = & \frac{- 2 x + 5}{5} \\ y & = & - \frac{2}{5} x + 1 \end{array}$

The second equation is already in slope-intercept form.

Step 3. Determine the slopes and y-intercepts.

For the first equation, $m = - \frac{2}{5}$ and the y-intercept is $(0, 1)$ .

For the second equation, $m = - \frac{2}{5}$ and the y-intercept is $(0, - 4)$ .

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 $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$ 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 2x+5y=5and y=-25x-4are 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 $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$ are parallel.