Sophie H.

asked • 09/28/17# Algebra 2 question

. Write the equation of a line perpendicular to the line 3x +7y =21 with a y-intercept of (0, 2). Write your answer in standard form.

Follow the steps below.

Step 1. Write the equation of the given line in slope-intercept form and determine its slope.

equation:

slope:

Step 2. Use the slope of the given line to determine the slope needed to write the equation of a perpendicular line and write a short paragraph explaining how you determined the slope of the perpendicular line.

slope needed for perpendicular line:

Reason:

Step 3. Write the equation of the perpendicular line on slope-intercept form and then write the equation in standard form.

slope-intercept form:

standard form:

Follow the steps below.

Step 1. Write the equation of the given line in slope-intercept form and determine its slope.

equation:

slope:

Step 2. Use the slope of the given line to determine the slope needed to write the equation of a perpendicular line and write a short paragraph explaining how you determined the slope of the perpendicular line.

slope needed for perpendicular line:

Reason:

Step 3. Write the equation of the perpendicular line on slope-intercept form and then write the equation in standard form.

slope-intercept form:

standard form:

More

## 1 Expert Answer

Hi Sophie.

To answer this as you teacher has suggested, slope-intercept form is y=mx+b. So solve the equation 3x+7y=21 for y.

Subtract 3x from both sides and get

7y = -3x + 21

Divide both sides by 7 and get

y = (-3/7)x + 3

From here you can see that the slope is (-3/7). The y-intercept is 3.

The perpendicular slope is found by changing the sign and "flipping" the fraction.

So the perpendicular slope is (+7/3).

The perpendicular line then is y = (7/3)x + 3

Putting that into standard form, we cannot use fractions, and the coefficient of x must be positive. So first I am going to multiply EVERYTHING by the denominator (3).

3y = 7x + 9.

Now subtract 3y from both sides.

0 = 7x - 3y + 9 (this keeps the coefficient of "x" positive)

Now subtact 9 from both sides.

-9 = 7x - 3y

You would be finished, but officially, standard form has the x- and y-terms on the left and the constant on the right, so let's flip this and the final answer, the way your teacher wanted you to work it, is

7x - 3y = -9

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

David W.

The parallel line, in Standard Form, is: 7x-3y=-609/28/17