Ok...i need help with this equation?

Question

, the coordinates are (2,2) (3,4)..the slope of them is 2. Now i know this equation: y=mx+b. i think i am suppose to find the y intercept or i am suppose to find b. im not sure and i dont know how to do either

Answer 1

The slope is 2, so that means m = 2
y = mx + b becomes
y = 2x + b
Now use either one of the given points to solve for b.
Suppose you use the point (2,2)
Replace x with 2 and replace y with 2
2 = 2(2) + b
2 = 4 + b
-2 = b
Answer: y = 2x - 2
Note: It doesn't matter which point you use. You will get the same value for b. Why don't you try it with the point (3,4). Replace x with 3 and y with 4 and then solve for b. You will get b = -2

Answer 2

if you have a point (2,2) and the slope is 2 (that's 2/1, understood as a rise of 2 and a run of 1), then the next point would be 2 up and 1 to the right, or (3,4). Inside the parentheses, the first number is the x value, the second the y. Since you have two sets of points and you can confirm that they are true values since you have also been given the slope, you already have all the information you need, simply draw the graph.


I know this can be confusing, even overwhelming at first. So keep working, and understanding will grow. And ask questions, I like to help people who are sincerely trying!

Answer 3

First of all, you know that the slope is 2. This means that "m = 2"

So, you know that

y = 2x + b

this on its own is not very helpful, but you have also been given two points that are on the line. Pick either one of them. Lets use (3, 4).

Well, all coordinates are given in the form (x, y). So, we also know that for one point on the line, "x = 3" and "y = 4".

So, our equation now becomes

4 = 2 ( 3) + b
4 = 6 + b
-2 = b

We have found the y intercept!

So, the equation of the line is y = 2x - 2 !

Answer 4

y intercept and b are the same thing, take this one step at a time, since yer at x=2 then you need to take it back 2 steps, one step back would put you at (1,0), then next step puts you at (0, -2). For exactly how to do this I'd ask your teacher more, but yer end equation is y=2x-2.

[The way I did that is for every time x increases by one positive unit, y increases by 2 positive units, so since I increased x by 2 negative units, or (simpler) I just went down two, I have to decrease my y by 4 (2x2=4).] Then I plug in everything to y=mx+b, y is a variable, it stays, x is a variable, it stays, m and b are both constants, so they change, we know m, it's 2, m=slope...so so far we have y=2x+b, then we get b, with everything that I did above in brackets, we get the idea that we simply subtract 4 from the y value of the point (2,2), so it's
2-4=-2. so our final equation is y=2x-2.

Oh another easy way to find b is to plug in your slope to the equation y=mx, no b, your y intercept is (0,0) or origin, then find the difference between the values of y that correspond with the x of the number you put in, example, you have the point (2,2) with the slope of 2, so you punch in y=2x, with origin as the y intercept, and you punch in 2 for x, you get 4, now (2,4) and (2,2) are not the same, but you put in the same x value for both, so what do you do? you subract your 1st y value (4) from your 2nd y value (2), and you get -2, and and that's your b value.

I hope you comprehend this and understand much better, if you don't ask your teacher and they should be able to help you. good luck.

Answer 5

The easiest way to find the equation for this line is to use the point-slope formula. If you know a point on a line and the line's slope, the following is always true, where the point that you know is (x1, y1):
y - y1 = m(x - x1)

Substituting the values from the point (2, 2), and the slope of 2:
y - 2 = 2(x - 2)
Then...
y - 2 = 2x -4
y = 2x - 2

This is the equation for this line. You can check the answer by plugging in the values of both of your points:
(2, 2):
y = 2x - 2
y = 2(2) - 2
y = 4 - 2
y = 2 --> Correct!

(3, 4):
y = 2(3) - 2
y = 6 - 2
y = 4 --> Correct!

Answer 6

b is the same as the y-intercept. You know m=2 so just plug either point into the equation to get b.