SOLUTION: Sorry I forgot to include the problem: APPENDEX D 485/32 Section 8.1 at the back of the book. Find an equation of each line. Write the equation using function notation.

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Question 198754This question is from textbook Intro & Inter Algebra
: Sorry I forgot to include the problem:
APPENDEX D 485/32 Section 8.1 at the back of the book.
Find an equation of each line. Write the equation using function notation.
Through (-4,8); perpendicular to 2x – 3y=1 This question is from textbook Intro & Inter Algebra

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y=1 Start with the given equation.


-3y=1-2x Subtract 2x from both sides.


-3y=-2x%2B1 Rearrange the terms.


y=%28-2x%2B1%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-2%29%2F%28-3%29%29x%2B%281%29%2F%28-3%29 Break up the fraction.


y=%282%2F3%29x-1%2F3 Reduce.


We can see that the equation y=%282%2F3%29x-1%2F3 has a slope m=2%2F3 and a y-intercept b=-1%2F3.


Now to find the slope of the perpendicular line, simply flip the slope m=2%2F3 to get m=3%2F2. Now change the sign to get m=-3%2F2. So the perpendicular slope is m=-3%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=2%2F3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-8=%28-3%2F2%29%28x--4%29 Plug in m=-3%2F2, x%5B1%5D=-4, and y%5B1%5D=8


y-8=%28-3%2F2%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-8=%28-3%2F2%29x%2B%28-3%2F2%29%284%29 Distribute


y-8=%28-3%2F2%29x-6 Multiply


y=%28-3%2F2%29x-6%2B8 Add 8 to both sides.


y=%28-3%2F2%29x%2B2 Combine like terms.


So the equation of the line perpendicular to 2x-3y=1 that goes through the point is y=%28-3%2F2%29x%2B2.


The equation in function notation would then be f%28x%29=%28-3%2F2%29x%2B2


Here's a graph to visually verify our answer:
Graph of the original equation y=%282%2F3%29x-1%2F3 (red) and the perpendicular line y=%28-3%2F2%29x%2B2 (green) through the point .

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Step 1: Solve the given equation for



Now that the equation is in slope-intercept form you can see that the slope of the given line is .

Step 2: Use the following rule to determine the slope of the desired line:



In other words, find the negative reciprocal of the slope of the given line.

Step 3: Use the given point and the slope you determined in step 2 to substitute values into the point-slope form of the equation of a line:



Where are the coordinates of the given point and is the slope you derived in step 2.

Since the problem only asks for 'an equation', you really don't have to do anything else, although typically you should either present the equation in slope-intercept () or standard () form.

John