SOLUTION: I'm suppose to find the equation of each line and write the equation using function notation: heres the problem: through (-4,8); perpendicular to 2x-3y=1 heres the work i have d

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Question 26593: I'm suppose to find the equation of each line and write the equation using function notation:
heres the problem:
through (-4,8); perpendicular to 2x-3y=1
heres the work i have done:
-3y = -2x+1 y=2/3x +1/3
slope = 2/3
y-8 = 2/3(x+4)
y+-8= 2/3x + 2 2/3
y=2/3x+-5 1/3
f(x)= 2/3x + -5 1/3
did i do this problem right or am i doing it completely wrong, please help, thanks
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Here's what I would do:
First, I would find the slope (which you did right)
The slope is 2%2F3
The work you did found the line that went through (-4,8), but wasn't perpendicular to 2x-3y=1. That was your mistake.
To find a perpendicular line, the slope will be the negative reciprocal.
So, the slope of your line will be -3%2F2.
To find the y-intercept, the easiest way is to plug the coordinates you already have back into slope-intercept form, which is y=mx%2Bb.
8=%28-3%2F2%29%2A-4%2Bb
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: b=2.
  • Graphical form: Equation 8=%28-3%2F2%29%2A-4%2Bb was fully solved.
  • Text form: 8=(-3/2)*-4+b simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+8=%28-3%2F2%29%2A-4%2Bb+%29
    For tutors: simplify_cartoon( 8=(-3/2)*-4+b )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 8=highlight_red%28+%28-highlight_red%28+3%2F2+%29%29%2A-4+%29%2Bb.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+1%2F2+%29
It becomes 8=-highlight_green%28+3+%29%2Fhighlight_green%28+2+%29%2A-4%2Bb.
Look at 8=-highlight_red%28+3+%29%2F2%2Ahighlight_red%28+-4+%29%2Bb.
Multiplied numerator integers
It becomes 8=-highlight_green%28+-12+%29%2F2%2Bb.
Look at 8=-highlight_red%28+-12%2F2+%29%2Bb.
Moved --12%2F2 to the right of expression
It becomes 8=b-highlight_green%28+-12%2F2+%29.
Look at 8=b-highlight_red%28+-12%2F2+%29.
Removed extra sign in front of 6
It becomes 8=b%2Bhighlight_green%28+6+%29.
Look at 8=highlight_red%28+b%2B6+%29.
Moved these terms to the left highlight_green%28+-b+%29,highlight_green%28+-6+%29
It becomes 8-highlight_green%28+b+%29-highlight_green%28+6+%29=0.
Look at highlight_red%28+8+%29-b-highlight_red%28+6+%29=0.
Added fractions or integers together
It becomes highlight_green%28+2+%29-b=0.
Look at highlight_red%28+2+%29-b=0.
Moved 2 to the right of expression
It becomes -b%2Bhighlight_green%28+2+%29=0.
Look at highlight_red%28+-b%2B2+%29=0.
Solved linear equation highlight_red%28+-b%2B2=0+%29 equivalent to -b+2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: b=2.

Universal Simplifier and Solver


Done!

So, you find that your y-intercept is 2.
The final formula in function notaion would be f%28x%29=-%283%2F2%29x%2B2
To check, graphing it may be helpful.
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-%283%2F2%29x%2B2%2C%282%2F3%29x-%281%2F3%29%29
The GREEN line is the original, and the RED line is the one you were trying to solve for.
From the graph, you can indeed see that the lines are parrallel.
Hope this helps!