Write an eqaution for the line- A line that pases through points (5, -4) and (2,2)?

Question

I dont get how to do this Please show all your work, right answer gets best answer

Answer 1

y+4/2+4=x-5/2-5
-3(y+4)=6(x-5)
-3y-12=6x-30
6x+3y-18=0
dividing by 3
2x+y-6=0

Answer 2

First we need to find the slope, denoted by "m."

m = change in y / change in x = (2 - (-4)) / (2 - 5) = 6 / -3 = -2

Then we can use point slope form: (y - y*) = m(x - x*).
Here x* and y* represent the x and y coordinates of any point on the line. So we have two choices: (2, 2) or (5, -4). Let's choose (2, 2).

Then our equation is: (y - 2) = -2(x - 2).

Done.

Answer 3

To start off with, the slope, m, is the measure of the change in y divided by the change in x. In general, that is (Y2-Y1)/(X2-X1). The order does not matter as long as your co-ordinates match up [as in (Y1-Y2)/(X1-X2) is ok, but (Y2-Y1)/(X1-X2) is not]. In this case, m=(-4-2)/(5-2)=-6/3=-2. The general equation for a line is Y=mX+b, so we know so far: Y=-2*X+b, meaning we still need to find b. This line passes through the 2 points given in the question, so we will use that point to find b, namely:
(2)=-2*(2)+b
2=-4+b
6=b
so our line will be: Y=-2X+6.
Just to be safe, we will check with the other point:
-4=-2*5+6. This is a true statement, so our line does indeed pass through both points

Answer 4

First: find the slope between the set of points:

formula > m = (second y - first y)/(second x - first x)
m = [2 - (-4)]/[2-5]
m = [2+4]/[2-5]
m = 6/-3
m = -2

Second: Take the slope, one set of points and place them into the slope intercept-formula: let's use points: (2,2):

y = mx + b
2 = -2(2) + b
2 = - 4 + b

Third: let's find the y-intercept, also known as "b" > add 4 to both sides:

2 + 4 = - 4 + 4 + b
6 = b; b = 6

Fourth: take the slope, y-intercept and place them into the slope-intercept formula:

y = -2x + 6

Answer 5

Slope: -4-2/5-2=-6/3=-2

y=-2x+b

Substitute a coordinate for the variables:

(2)=-2(2)+b
2=-4+b
+4 +4

6=b

Your equation for this line is:

y=-2x+6

Answer 6

I'm gonna give you the answer but you really should be reading your text book.

First you need to know the formula, which is m=Y2-Y1/X2-X1.

(X1,Y1) and (X2, Y2)

So then Y2-Y1 = 2-(-4)
AND X2-X1 = 2-5

2-(-4)/2-5= 6/-3 = -2

Next formula you need to know is y=mx+b

so you take one of the points (any point) and plug that into the formula along with the new slope (m).

-4=-2(5)+b

-4=-10+b

Add 10 to each side. -4 + 10 = 6

6 = b

So now you have to plug that number into the equation y=mx+b

Answer:

y= -2x+6

Answer 7

A. (x - 5, y - 4), B. (x - 2, y - 2)

subsitute x and y for two equations - double letter algebra
y=mx+b
A. 4=5m +b
B. 2=2m+b

Therefore: 4=5m+2-2m (both points are on the same line)
(for B: 2-2m is equal to b, so it's still 4=5m+b)
now you solve the equation

4=5m+2-2m
4=3m+2
2=3m
m=2/3
b=2/3

verify with both equations: 4=5(2/3)+2/3
2=2(2/3)+2/3

They work!

so therefore, equation is: y=2/3x + 2/3

hope this helps:)