In class on Friday, we continued the problem on finding the point of intersection.
The point of intersection is where two sets of data break even. In a table, the two columns are the same at the same value of x, and on a graph, the two sets break even when the two lines intersect., and in an equation you make each equation equal the other and then solve for the variable. In the problem with Fabian's Fabulous Bakery, the equation for his expenses was E=825+3.25n, and the equation for his income was I=8.20n. In this case, the point of intersection is where Fabian no longer owes any money and is ready to start making a profit. To use the equation, you would put the expression for his expenses on one side and the expression for his income on the other side, and then solve for the variable. The equation to find the break even point for Fabian would be 825+3.25n=8.20n. The solution is 166 2/3, so Fabian would have to sell 167 cakes to be out of debt because he cannot sell 2/3 of a cake.
Post by: Peter S.
Sunday, November 15, 2009
Thursday, November 12, 2009
Y-Intercepts and Coefficients
Today we continued the work we did yesturday on y-intercepts and coefficints.
To review, the y-intercept is the point were the line crosses the y axis, and the coefficient is the number multiplied by the variable. In the Emile and Henri problem, Henri's equation is d=1t+45. 1 is the coefficent of t, and the y-intersect is 45.
Using this we started Problem 3.5 on page 55. This problem was about Finding the Point of Intersection.
"At Fabulous Fabians's Bakery, the expenses E to make n cakes per month is given by the equation E=825 +3.25n. "
In this equation, we are identifying things like the y-intercept (825), and th coefficient (3.25) and finding the income using another formula I=8.2n.
Allie G.
To review, the y-intercept is the point were the line crosses the y axis, and the coefficient is the number multiplied by the variable. In the Emile and Henri problem, Henri's equation is d=1t+45. 1 is the coefficent of t, and the y-intersect is 45.
Using this we started Problem 3.5 on page 55. This problem was about Finding the Point of Intersection.
"At Fabulous Fabians's Bakery, the expenses E to make n cakes per month is given by the equation E=825 +3.25n. "
In this equation, we are identifying things like the y-intercept (825), and th coefficient (3.25) and finding the income using another formula I=8.2n.
Allie G.
Tuesday, November 10, 2009
Problem 2.3 Comparing Costs
Today we learned about the y-intercept. Here are some useful definitions:
y-intercept: the point where the line crosses the y-axis on a graph or when x=0 in a table (the starting point)
coefficient: the rate of change AND/OR the number that multiplies a variable in an equation
In the equation y=mx+b, y=the dependant variable, m=the coefficient and/or rate of change, x= the independent variable, and b=the y-intercept.
Here's another example, using the problem with Emile and Henri that we did yesterday in class.
Henri's equation: d=1t+45
The coefficient of t is 1 and the y-intercept is 45
Emile's equation: d=2.5t
The coefficient of t is 2.5 and the y-intercept is 0.
If no y-intercept is stated in the equation (that means there is no addition), it is assumed to be 0.
y-intercept: the point where the line crosses the y-axis on a graph or when x=0 in a table (the starting point)
coefficient: the rate of change AND/OR the number that multiplies a variable in an equation
In the equation y=mx+b, y=the dependant variable, m=the coefficient and/or rate of change, x= the independent variable, and b=the y-intercept.
Here's another example, using the problem with Emile and Henri that we did yesterday in class.
Henri's equation: d=1t+45
The coefficient of t is 1 and the y-intercept is 45
Emile's equation: d=2.5t
The coefficient of t is 2.5 and the y-intercept is 0.
If no y-intercept is stated in the equation (that means there is no addition), it is assumed to be 0.
Moving Straight Ahead problem 2.3 - y=mx + b
Notes from today's lesson on the y = mx + b form of linear equations.
Moving Straight Ahead 2.3
View more presentations from Kathy Favazza.
Monday, November 9, 2009
Problem 2.1 Finding the Point of Intersection
Today in class we learned how to find the variable so that the two equations are equal. This is the problem that we focused on.
In Ms. Chang's class, Emile found out that his walking rate is 2.5 meters per second. When he gets home from school, he times his little brother Henri as Henri walks 100 meters. He figured out that Henri's walking rate is 1 meter per second.
Henri challenges Emile to a walking race. Because Emile's walking rate is faster, Emile gives Henri a 45-meter head start. Emile knows his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his brother will win. How long should the race be so that Henri wins a close race?
One option is to use a graph. First, you plot the points to represent how far they have walked after every ten meters and connect them. Then you look to see where the two lines intersect to find the distance they will have to walk to meet. If you subtract a meter from that, Henri will only win by a little. The lines on the graph intersect at 75 meters so if you subtract one and make it 74, Henri will win a close race.
Another option is to use a table. This is what it would look like:
Time___Emile __Henri
_ 0 ____ 0______45
_10____ 25_____ 55
_20____ 50_____65
_30____ 75_____75
_40____100____ 85
(The time is in seconds and the data under Emile and Henri represent how far they have walked in meters.)
After 30 seconds they meet at 75 meters. If you make the race 74 meters, Henri will win but just by a little.
A third option to solve this is to use an equation. That is what I did.
2.5x = 1x + 45
2.5x - 1x = 1x + 45 - 1x
1.5x = 45
1.5x / 1.5 = 45 / 1.5
x = 30
2.5 = Emile's walking rate
x = seconds
1 = Henri's walking rate
45 = Henri's starting point
After 30 seconds they will meet. To figure out how far they will be from the starting point you have to do the check:
2.5(30) = 1(30)+45
75 = 30+45
75 = 75
After you do the check you figure out that at 75 meters they will meet. You need to subtract a meter so that Henri will win. After they have walked 74 meters, Henri will only be ahead by a little so he would win a close race.
From the graph, table and equation you can figure out that they will meet after 30 seconds at 75 meters. For Henri to win a close race, it would have to be 74 meters long.
Post by: Alex S.
In Ms. Chang's class, Emile found out that his walking rate is 2.5 meters per second. When he gets home from school, he times his little brother Henri as Henri walks 100 meters. He figured out that Henri's walking rate is 1 meter per second.
Henri challenges Emile to a walking race. Because Emile's walking rate is faster, Emile gives Henri a 45-meter head start. Emile knows his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his brother will win. How long should the race be so that Henri wins a close race?
One option is to use a graph. First, you plot the points to represent how far they have walked after every ten meters and connect them. Then you look to see where the two lines intersect to find the distance they will have to walk to meet. If you subtract a meter from that, Henri will only win by a little. The lines on the graph intersect at 75 meters so if you subtract one and make it 74, Henri will win a close race.
Another option is to use a table. This is what it would look like:
Time___Emile __Henri
_ 0 ____ 0______45
_10____ 25_____ 55
_20____ 50_____65
_30____ 75_____75
_40____100____ 85
(The time is in seconds and the data under Emile and Henri represent how far they have walked in meters.)
After 30 seconds they meet at 75 meters. If you make the race 74 meters, Henri will win but just by a little.
A third option to solve this is to use an equation. That is what I did.
2.5x = 1x + 45
2.5x - 1x = 1x + 45 - 1x
1.5x = 45
1.5x / 1.5 = 45 / 1.5
x = 30
2.5 = Emile's walking rate
x = seconds
1 = Henri's walking rate
45 = Henri's starting point
After 30 seconds they will meet. To figure out how far they will be from the starting point you have to do the check:
2.5(30) = 1(30)+45
75 = 30+45
75 = 75
After you do the check you figure out that at 75 meters they will meet. You need to subtract a meter so that Henri will win. After they have walked 74 meters, Henri will only be ahead by a little so he would win a close race.
From the graph, table and equation you can figure out that they will meet after 30 seconds at 75 meters. For Henri to win a close race, it would have to be 74 meters long.
Post by: Alex S.
Moving Straight Ahead
Lesson on linear functions using tables, graphs & equations.
Moving Straight Ahead 2.1 & 2.2
View more presentations from Kathy Favazza.
Tuesday, November 3, 2009
Moving Straight Ahead
Notes on Moving Straight Ahead - linear relationships.
Moving Straight Ahead
View more presentations from Kathy Favazza.
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