Finding an equation in an x y coordinate system...?

Question

Can you find an equation that passes through the points <2,8>, and a line that passes perpendicular to 2x - 3y = 12. Explain how you get to your answer step by step, and good luck!

Answer 1

You can find the slope of 2x - 3y = 12, call it m. The line perpendicular to it will have slope -1/m. Since you know the slope (-1/m) of your line and a point on it (2,8) you can solve to find the equation.

STEP 1 -- Find -1/m

2x - 3y = 12
-3y = -2x - 12
y = 2/3 x - 4 << so m=2/3, and -1/m = -3/2

STEP 2 -- Use slope -3/2 and point (2,8) to find the equation

Recall that (y-y0)=m(x-x0), so we get the following:

y - 8 = -3/2 (x - 2)
y - 8 = -3/2 x + 3
y = -3/2 x + 11

So, the equation you are looking for is y = -3/2 x + 11

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Answer 2

The line y=8 is a horizontal line that passes throur the point (2,8). And as for your second question, start by putting the equation in slope intercept form: y=2/3x-4; since the slope of this line is 2/3, the slope of the line which is perpendicular to this would have slope -3/2. If you want the equation of the line that passes through (2,8) and is perpendicular to the given equation, use the point slope formula: y-8=-3/2(x-2)
y=-3/2x+11.

Answer 3

first of all, you can use the slope intercept equation y=mx+b
Solving for y you get the following:

-3y=-2x+12
y= -2/3x-4
slope (m)is equal to -2/3 y intercept (b)= -4
when you graph this you can use the y intercept as your first point (0,-4)
the use the slope to find a second point (remeber slope is rise over run so you would start at popint (0,4) and would go down 2 and to the right 3 or up 2 and tho the left 3. Either way, you draw a line between the points and this is your line.
A perpendicular line will have a slope that is the inverse and opposite sign of the slope of that line. Therfore a perpendicular should have a slope of 3/2.
Now an equation that passes through the point (2,8) is easy.
Remember y=mx+b ? make up any other point ie (1,4)
Well m= y2-y1/x2-x1 so.... y2=8 y1=4 x2=2 x1=1
substitute and you get m= 8-4/2-1= 4
so... y=mx+b 8=4 times 2 +b therfore b=0

Answer 4

2x- 3y = 12
3y = 2x-12

Divide both sides of the equation by 3 to get:

y = 2/3x - 4
We now have the equation of the line in slope form, where the gradient is 2/3.

for two perpendicular lines, the product of their gradient is equal to -1. therefore gradient of unknown line = -3/2

the unknown line will now have an equation of the form:
y= -3/2x + c, where c is the y-intercept.

to find c, we will substitue x=2, y=8 into the above equation:

8 = (-3/2)(2) + c
c = 11

therefore the line is given by y = -3/2x + 11