Help with hard math question?

Question

I need help with my math homework. Its just to confusing. Will someone please help me? I would appreciate it so much!!
Suppose (x1,y1) and (x2,y2) are two points. Do the following:
(a) Find the slope of the line that contains the two points.
(b) Find the x- and y-intercepts.
(c) Find the equation of the line in slope-intercept form.
Include as much detail as possible.
Any ideas?

Answer 1

The equation for a line is:

y = mx + b

You know a line is a infinite number of points, but between any two points there is only one unique line. This problem would have been much easier if your teacher just gave you two points (like (3,5) and (-2,4) for example), but in this form it is much more powerful because you'll get the general form for ANY two points.

Ok, how to solve: Point 1 just has the coordinates (x1,y1), but you know it has to fit into the linear equation. So plug in:

y1 = mx1 + b

Do the same for the second point:

y2 = mx2 + b

You have 2 equations and 2 unknowns. Solve for m and b:

First subtract the two equations to solve for m:

y1 = mx1 + b
-y2 = -mx2 - b

(y1-y2) = (x1-x2)m

m = (y1-y2)/(x1-x2)

Now plug into the first equation and solve for b:

y1 = [(y1-y2)/(x1-x2)]*x1 + b

b = y1 - [(y1-y2)/(x1-x2)]*x1

So the full equation for the line, which can contain any x,y that fits the equation, is:

y = [(y1-y2)/(x1-x2)]*x + y1 - [(y1-y2)/(x1-x2)]*x1

Remember that x and y correspond to any point on the line, and the m and b we found because we knew 2 points, (x1,y1) and (x2,y2)

The slope is m. The x intercept is where y = 0, and the y intercept is where x = 0 (which you'll notice is just b which you found).

Hope this helps. And unlike that fool who claims this is a stupid problem, this is actually an excellent problem. Not only do you now have the solution for ANY two points, so that you NEVER have to do this equation again, far more importantly these exercises are teaching you how to think critically. Even if you never go into the sciences it is important to learn how to reason and go through problems step-by-step. You'll be tested on it in high school, college, the SAT, the GRE and in any job you take. Only an idiot would disregard math. Good luck.

Answer 2

If we are given two points (x1, y1) and (x2, y2) and we want to find the slope between them we only need to remember that slope is rise-over-run.

Slope is a fraction, for a particular distance, say 10 feet, if we go up 2 feet then the slope is 2/10, or simplified as 1/5. This is the same as the signs on the roads in the mountains. We see a sign, "Trucks, 3% grade." Here they prefer to use the term grade instead of slope, but it's the same thing. A percentage is a fraction too. 3% = 3/100. So, a 3% grade is going up 3 feet for every 100 feet across.

Ok, back to our problem. How can we find the rise? If we subtract the second pont from the first point then we will have the difference between them. So, the "rise" is y2-y1. It doesn't matter which is larger. If the second point(y2) is larger the the result will be positive, meaning we go up. If the second point is smaller, the result will be negative and we go down.

Now for the "run." We can do the same thing. Here order does matter, but points are always listed left to right. If x2 is larger than x1, then blame your teacher for writing the points backwards. So the difference is (x2-x1).

Then, the slope between our two points is the fraction (y2-y1)/(x2-x1). Yeah!

Now, the equation of a line is: y=mx+b

m is the slope, b is the y-intercept.

Let's add in our slope.

y = [(y2-y1)/(x2-x1)]x + b

Let's try to find the y-intercept called "b"

We need a point on the line. Hmmmm... Hey! The problem gave us two points on the line. We can choose either (x1, y1) or (x2, y2).

Let's choose the first and plug it into our equation.

y1 = [(y2-y1)/(x2-x1)](x1) + b

y1 - (y2-y1)(x1)/(x2-x1) = b

Ok, I know this looks complicated, but it's only because we don't know the points so we can't perform the simple calculations. And, by the way, this is the y-intercept.

Plug this into into the equation to find the full equation in intercept form

y = [(y2-y1)/(x2-x1)]x + y1 - (y2-y1)(x1)/(x2-x1)

Finally, to find the x-intercept, set y = 0. Whenever y=0 you're somewhere on the x-axis.

0 = [(y2-y1)/(x2-x1)]x + y1 - (y2-y1)(x1)/(x2-x1)

Let's subtract our y-intercept...

-y1 + (y2-y1)(x1)/(x2-x1) = [(y2-y1)/(x2-x1)]x

and now divide both sides by the slope.

[-y1 + (y2-y1)(x1)/(x2-x1)]/[(y2-y1)/(x2-x1)] = x

And there we go.

Answer 3

a million+a million=2 moreover, somebody with a tactics too lots time on their palms desperate to tutor it... "The evidence starts off from the Peano Postulates, which define the organic numbers N. N is the smallest set pleasurable those postulates: P1. a million is in N. P2. If x is in N, then its "successor" x' is in N. P3. there's no x such that x' = a million. P4. If x isn't a million, then there's a y in N such that y' = x. P5. If S is a subset of N, a million is in S, and the implication (x in S => x' in S) holds, then S = N. then you definitely would desire to define addition recursively: Def: enable a and b be in N. If b = a million, then define a + b = a' (employing P1 and P2). If b isn't a million, then enable c' = b, with c in N (employing P4), and define a + b = (a + c)'. then you definitely would desire to define 2: Def: 2 = a million' 2 is in N by employing P1, P2, and the definition of two. Theorem: a million + a million = 2 evidence: Use the 1st part of the definition of + with a = b = a million. Then a million + a million = a million' = 2 Q.E.D. observe: there is yet another formula of the Peano Postulates which replaces a million with 0 in P1, P3, P4, and P5. then you definitely would desire to alter the definition of addition to this: Def: enable a and b be in N. If b = 0, then define a + b = a. If b isn't 0, then enable c' = b, with c in N, and define a + b = (a + c)'. you moreover mght would desire to define a million = 0', and a couple of = a million'. Then the evidence of the theorem above is a splash diverse: evidence: Use the 2nd part of the definition of + first: a million + a million = (a million + 0)' Now use the 1st part of the definition of + on the sum in parentheses: a million + a million = (a million)' = a million' = 2 Q.E.D." Wow, he would desire to be a real hit with the girls...!! :)

Answer 4

line: y=mx + b : y=x+1
slope: m = 1
y intercept: = 1
x intercept = 1

slope:
y2-y1 / x2 - x1 ==== 2-1 / 2-1 ==== 1/1 ==== 1

line:
y=mx+b
1=m1+1
0=m1
m=0

Answer 5

a) You find the slope by using the definition of slope:
m = (y2-y1)/(x2-x1)
b) Derive the equation for the line in point-slope form:
(y - y1)/(x - x1) = (y2-y1)/(x2-x1)
(y - y1) = ((y2-y1)/(x2-x1))(x - x1)
x-intercept is when y = 0:
-y1 = ((y2-y1)/(x2-x1))(x - x1)
x = x1 - y1(x2-x1)/(y2-y1)
y-intercept is when x = 0:
y = y1 - x1(y2-y1)/(x2-x1)
c)
Changing to slope-intercept form:
(y - y1) = ((y2-y1)/(x2-x1))(x - x1)
y = ((y2-y1)/(x2-x1))x + (y1(x2-x1) - x1(y2-y1))/(x2-x1)

Answer 6

I wouldn't even bother answering it...give me an example of an algebra problem in every day life.......? that s**t's useless.. you pay for you education...ask them to teach you something worth learning....!