linear equations help.point passes thre line?

Question

1.the line that passes through
(1,1)and (3,4)
my answer always comes out wrong
_ _ _ _ _=_

2.(-3,5) and (-2,-6)
_ _ x_ _=_ _ _

im usually short on teh blanks or have to many help me solve please.thankyou

Answer 1

1. y=(3/2)x-(1/2)
2. y=-11x-28

Answer 2

First find the slope (rise over run) of the line.
The rise equals 4 - 1 = 3; the run = 3 - 1 = 2
The slope is therfore 3/2 or the ratio/fraction 3 over 2.

Using the point slope form and (1,1)
you get y - 1 = 3/2( x - 1)
distribute on the right hand side y - 1 = 3/2 x - 3/2
add 1 to each side
y = 3/2 x - 3/2 + 1
y = 3/2 x - 3/2 + 2/2
or y = 3/2 x - 1/2 (SLOPE INTERCEPT FORM)
------------------------------------
Using the second point (3,4)
you get y - 4 = 3/2 ( x - 3)
distributing on the RHS y - 4 = 3/2 x - 9/2
add 4 to each side y = 3/2 x - 9/2 + 4
or y = 3/2 x - 9/2 + 8/2
or simply y = 3/2 x - 1/2 (SLOPE INTERCEPT FORM)

You the same equation whether you use (1,1) or (4,3)
but remember to find the slope first.

In problem 2, the rise is -6 - 5 = -11
the run is -2 - -3 = 1
The slope is -11/1 or -11

Using the point slope form
y - 5 = -11 ( x - -3)
y - 5 = -11 (x + 3)
y - 5 = -11x - 33
Add 5
y = -11x - 33 + 5
y = -11x -28 (SLOPE INTERCEPT FORM)

Answer 3

1) Line that passes through (1, 1) and (3, 4)

Our ultimate goal is to have a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Your first step is to use the slope formula;
m = (y2 - y1)/(x2 - x1)

With (x1, y1) = (1, 1) and (x2, y2) = (3, 4)

m = (4 - 1)/(3 - 1)
m = 3/2, which tells us the slope is equal to 2.

Now, use the slope formula again, with (x1, y1) = (1, 1) and (x2, y2) = (x, y).

(y2 - y1)/(x2 - x1) = m
(y - 1)/(x - 1) = 3/2

y - 1 = (3/2)(x - 1)
y - 1 = (3/2)x - (3/2)
y = (3/2)x - (3/2) + 1
y = (3/2)x - (3/2) + (2/2)
y = (3/2)x - 1/2

Try the second question on your own.