Algebra 2 question

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:

Answer 1

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