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Slope Intercept Form
Transcript of Slope Intercept Form
Hon. Alg II project
March 18 2011 By: Brycen K. + DaeShaun S. In the formula Y=mx+b , m is the slope (which is rise over run) And b is the y intercept (where the line crosses the y axis)
The X and Yare any given point on the line. IN OTHER WORDS..
m tells you how to move and b tells you where to start. LETS TRY THIS THANG! You might get a problem like this..... Solve for Y and use the resulting equation to find the slope of a line.
-3x+y=9 This is what you would do! -3x+y=9 You get the Y on a side by itself to get the equation in slope intercept form. Its Simple! Now all you do is look at the equation and tell what the slope is.. Remember before we said that the m was the number that means slope. In the equation m was next to X so whatever number is next to x is the slope! In our problem above, 3 is next to X so that makes it the slope. Hint: Since the slope is rise over run, if the number is not already a fraction, you should but it as a fraction making the denominator 1. The top number is the rise (how far up you go) and the bottom is the run(the distance left and right you go.) +3x +3x y=3x+9 Somtimes you might get a problem that wants you to graph the line using slope intercept form. Sounds hard? Dont worry. Its a piece of cake! LETS GIVE IT A TRY Using y=3x+9 , Graph a line. First you will mark your Y intercept on the y axis. In our case it is a +9 so we will go up on the Y axis 9 times. This will be the point you start your line at. From here you use the slope to make the line. In our case we will be moving up 3 and over one. (Rise over run). Since lines never end, you can go the same rise over run in the opposite direction. And there goes your line :) Somtimes you might have to take the information about a line and write it in slope intersept form. Confusing ? Lets try it.! Write an equation in slope intercept form for the line that passes through the point (6,4) and is parallel to the line with the equation Y=-2x-3. HInt: If a line is parallel they have the same slope. You got to try to get the Y=mx+b form so you plug in what you got and solve for the missing values.. Like this. Y=mx+b Y=4 X=6 m=-2
4=(-2)(6)+b You use the point they give you and plug it in for X and Y (duhh) And use the slope of the parallel line for m. Since they didnt give us b, that will be the term you slove for. 4=-12+b
+12 +12 16=b You solve it just like a regular math equation and find out that the value of b is 16! Now you have the slope of the line (2) and the y intercept (16) so you can write the equation.
If the problem asks you to graph this you would go up 16 times on the Y axis and mark it then go down 2 and right one. ANOTHER HINT: If the slope is negative the line will point in the opposite direction. Lets say the slope of a line is -7 and the y-int is 3. To graph this line you go up 3 on the y-axis and then down 7 and one over to the left. If the 7 would have been possitive you would have went right instead of left. This is the direction a possitive sloping line should go. And this is the direction a negative sloping line should go LETS SUM IT ALL UP! Slope intercept form(Y=mx+b) is the formula for a line. The X and Y are any point on the line and the m is the slope(rise over run). B is the Y- Intercept(Where the line crosses the y axis). The ways to solve slope intercept problems is by taking the equation of a line and graphing it using the slope and y int. The other way to solve it wa by taking the information given to you and solving for missing values to get the equation y=mx+b. You may also get a line and have to take the information off the line to get the equation.
LETS DO THISS!!! On this line we can see that the Y int. is 2 because that is where it crosses the y axis. The slope of this line is 1 because if you go up one and over one you will touch the line.. In that case, the equation of this line would be Y=1x+2. EASY AS 123 And the other way to solve Slope intercept form problems is by using a line and getting the information off of it to get the equation y=mx+b WORD PROBLEMS!! You are visiting Baltimore MD, and a taxi company charges a flat fee of $3 for using the taxi and an additional .75c per mile. Write an quation that you could use to find the cost of a taxi ride. Let X represent the number of miles and Y represent the total cost.
How much would a 8 mile ride cost. OKAY. You are trying to take the information given and make a Y=mx+b equation. The flat fee in the problem will be the Y int.(b) because it is only added once and stays the same. The .75c will be the slope(m) because it will be multiplied to the amount of miles. (also the word per means its the slope.). So here is our equation.
The problem asks us to find the price of a 8 mile taxi ride. Its simple. Just put the 8 in the place of the x and multiply. Y=(.75)(8)+3
Y= 9 PROBLEM SOLVED! Lets try a few more word problems. A plumber charges a few if 50 dollars to make a house call. He also charges 25 dollars an hour for labor. Write an equation to model the above situation. Let x represent the # of houes for labor and y represent the total cost.
How much is it for a house call that requires 2.5 hours of labor? Answer : Y=25x+50
$112.50 A mutual fund company charges 50 dollars a year to hold the fund and then an additional 2%(.02) of the profits made for that year. Write and equation that can be used to determine how much one would pay to the mutual fund company in a year. X= profit Y=Total cost.
What if the yearly profit was 1800? Answer: Y=.02x+50
Slope intercept form started out as x/a + y/b = 1 but modernated over time.
It is not known who discoverd slope intercept but it is thought to be a French person be cause of m meaning slope and the word monter means to clind in french.
Slope intercept form has been around for a very long time because Descartes used it in one of his lituratures in 1637
Write the following in slope intercept form.
Y=2/3x-3 Write an equation in slope intercept form for the line that satisfies the following condition. The slope is 5 and a point on the line is (2,12) ANSWER:
y=5x+2 Graph the equation from above. ANSWER: Use the information off this line to find the equation. ANSWER:
Y=1x+3 THANKS FOR PAYING ATTENTION. NOW LETS TAKE A LOOK AT THIS COOOL RAP