Write the equation of the line...

[Brenten]

Write the equation of the line having the following points:

x: -2 , 0 , 2 , 4
y: -9 , -5 , -1 , 3

For starters, I did m = y2-y1
-------
x2-x1

For m = -9 +2 = -7 = 2 1/3
------ ---
-2 -1 = -3

Therefore, y+9 = 2 1/3(x+2)

Am I even close?

 

[tutor_joel]

x: -2 , 0 , 2 , 4
y: -9 , -5 , -1 , 3

I'm not sure what this means. Do you mean the points (-2, -9), (0, -5)...etc

each x value must be associated with a y value. In which case you will use the equation for a line (y-y1)/(x-x1) = (y2-y1)/(x2-x1)

 

[Brenten]

Yes, those are the points. I took two sets of points to make the M = rise over run.

 

[tutor_joel]

in that case, using the equation above,

x1 = -2
x2 = 0
y1 = -9
y2 = -5

for example. you can use any 2 of the 4 points.

 

[Deleted member 4993]

Write the equation of the line having the following points:

x: -2 , 0 , 2 , 4
y: -9 , -5 , -1 , 3

For starters, I did m = y2-y1
-------
x2-x1

For m = -9 +2 = -7 = 2 1/3
------ ---
-2 -1 = -3

Therefore, y+9 = 2 1/3(x+2) <<< that is not correct - Which two points are you choosing

Am I even close?

 

[tutor_joel]

Yeah, sorry, I guess I should have looked at the answer

 

[Brenten]

Ok, when I do that I get -5 -(-9) / -2 -(0) which then gives me -5 +9 (or +4) over -2
which becomes +4 / -2 which is my rise (+4) over run (-2) ?

 

[mmm4444bot]

when I [use the Slope Formula] I get [-5 -(-9)] / [-2 -(0)]

Please type grouping symbols around numerators and denominators (as shown in red above).


which becomes +4 / -2 The sign is wrong. This should be 4/2, which reduces to 2.

You transposed your values for x[sub:3lhpfo37]2[/sub:3lhpfo37] and x[sub:3lhpfo37]1[/sub:3lhpfo37], so your slope has the wrong sign.

In other words, you calculated x[sub:3lhpfo37]1[/sub:3lhpfo37] - x[sub:3lhpfo37]2[/sub:3lhpfo37] instead of x[sub:3lhpfo37]2[/sub:3lhpfo37] - x[sub:3lhpfo37]1[/sub:3lhpfo37], in the denominator of the Slope Formula.

Here is the correct set-up:

\(\displaystyle m = \frac{-5 - (-9)}{0 - (-2)}\)

 

[Brenten]

Ok, I see what I did wrong there. By the way, how did you get that equation to look like that in the post? Some sort of math type program?

So now my M=2. Does that mean my equation of the line would be y-9 = 2(x-2) ?

 

[tutor_joel]

Starting with

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)


This states that, for a given straight line, the slopes are equal at any two points ie. m1 = m2

The unknowns in the above equation are the x and y terms. The known terms are the x1, x2, y1 and y2 terms from any two points on the line (x1, y1), (x2, y2).

Plug in all known values and rearrange to slope intercept form. y = mx + b

 

[mmm4444bot]

So now my M = 2. Does that mean my equation of the line would be y-9 = 2(x-2) ? Nope. You forgot the negative signs on that particular pair of given x- and y-coordinates.

\(\displaystyle y - [-9] = 2(x - [-2])\)

The "pretty-print" math formatting used here is a variant of the well-known math-typesetting software known as LaTex.

You can read about it HERE.

You can also click the

button on any post that contains LaTex, to view what the actual coding looks like.