SOLUTION: Write an equation in slope-intercept form of a line with the following characteristics: parallel to the graph of: -4x + 3y= 12 and passes through the origin.

Algebra ->  Absolute-value -> SOLUTION: Write an equation in slope-intercept form of a line with the following characteristics: parallel to the graph of: -4x + 3y= 12 and passes through the origin.      Log On


   

Question 175881This question is from textbook
: Write an equation in slope-intercept form of a line with the following characteristics: parallel to the graph of: -4x + 3y= 12 and passes through the origin. This question is from textbook

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the origin is the point (0,0)


-4x+%2B+3y=+12 Start with the given equation.


3y=12%2B4x Add 4x to both sides.


3y=4x%2B12 Rearrange the terms.


y=%284x%2B12%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%284%29%2F%283%29%29x%2B%2812%29%2F%283%29 Break up the fraction.


y=%284%2F3%29x%2B4 Reduce.


We can see that the equation y=%284%2F3%29x%2B4 has a slope m=4%2F3 and a y-intercept b=4.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=4%2F3.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=4%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-0=%284%2F3%29%28x-0%29 Plug in m=4%2F3, x%5B1%5D=0, and y%5B1%5D=0


y=%284%2F3%29%28x-0%29 Simplify


y=%284%2F3%29x%2B%284%2F3%29%280%29 Distribute


y=%284%2F3%29x%2B0 Multiply


y=%284%2F3%29x Simplify



So the equation of the line parallel to -4x+%2B+3y=+12 that goes through the point is y=%284%2F3%29x.


Here's a graph to visually verify our answer:
Graph of the original equation y=%284%2F3%29x%2B4 (red) and the parallel line y=%284%2F3%29x (green) through the point .


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The origin is the point (0,0). This point must
solve the equation
The line given is
-4x+%2B+3y+=+12
I'll put it in slope-intercept form
3y+=+4x+%2B+12
y+=+%284%2F3%29x+%2B+4
The general form is
y+=+mx+%2B+b where m is the slope, so
m+=+4%2F3
Going back to the general form, I can write
y+=+%284%2F3%29x+%2B+b
To find b, plug (0,0) into the general equation
0+=+%284%2F3%29%2A0+%2B+b
b+=+0, so the answer is
y+=+%284%2F3%29x+%2B+0
y+=+%284%2F3%29x+