geomtry help. pleaseee.?

Question

determine whether each pair of lines is parallel, perpenicular, or neither. If they intersect, find their point of intersection.

y= 4/3x -5
y= 3/4x + 2
my answer: the lines intersect and the point of intersection is (12, 11). please tell me if my answer is correct or wrong. and if you can please explain.

how do i determine the equation in slope intercept form for a line with endpoints (-5,8) and (8,2).
i think the y intercept is (0,6) but i cant find the slope.

Answer 1

They aren't parallel or perpendicular because of their slopes.

Test to see where they intersect...
Set the two equations equal to each other:
(4/3)x - 5 = (3/4)x + 2

Multiply both sides by 12:
16x - 60 = 9x + 24
7x = 84
x = 12
y = (4/3)(12) - 5
= 11

So you are correct!


For the second part:

Find the slope using rise over run:
(y2 - y1) / (x2 - x1)
= (2 - 8) / (8 - (-5))
= -6/13

Now use point-slope formula:
y - y0 = m(x - x0)
y - 8 = (-6/13)(x + 5)
y - 8 = -6x/13 - 30/13
y = -6x/13 - 30/13 + 8
y = -6x/13 - 30/13 + 104/13
y = -6x/13 - 74/13

Answer 2

The lines aren't parallel, because they don't have
the same slope.
They aren't perpendicular because their
slopes aren't negative reciprocals.
(Or: The product of their slopes is not -1.)
So the answer to the question is neither.
Where do the lines intersect?
Where 4/3x - 5 = 3/4x + 2.
7/12 x = 7
x = 12
Plugging this into each equation for y,
we find y = 11.
So your point of intersection is correct.
Last question:
The slope is the difference of the y's divided
by the difference of the x's.
So
m = -6/13
y = -6x /13 + b
Now plug in either point to get b:
2 = -48/13 + b
b = (26+48)/13 = 74/13.
y = -6x/13 + 74/13.
Check: Is (-5,8) on the line?
Plug it in and check:
If x = -5,
y = (30+74)/13 = 104/13 = 8,
so our equation is correct.

Answer 3

Yes you are right on in the 1st question.

The slope is (8-2)/(-5-8) = - 6/13