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¶ … Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain.
If a line on a Cartesian graph is approximately the distance y in feet that a person walks in x hours, then there would be a 1:1 correspondence between the x and y coordinates, so that the equation for the line would be y=x, and the slope of the line would be 1. The equation for the line can be seen below:
(Harmsworth, 2012).
The graph is useful because it helps demonstrate the one to one correspondence between the two variables, and makes it clear that for each additional hour (x) spent walking, the person travels an additional set distance in feet (y). However, it is unlikely that this equation would actually represent a person's distance in feet over a certain number of hours. Expanding the graph, one would expect to see a decline in feet per hour as exhaustion set in for the walker. As a result, it is important to realize that this standard graph has some limitations. Another example of this type of one to one graphical equation would be that for...
This line is going to be a vertical line and must run parallel to the y-axis; because, otherwise the equation would include a value at which x would be zero. The form of the equation for such a line will be x= a number. In the example below, the equation would be x=5.
(Rehill, 2012).
What if a line has no x-intercept?
If a line has no x-intercept, then there is no value of x for which the y would be zero. This line is going to be a horizontal line and must run parallel to the x-axis; because, otherwise the equation would include a value at which y would be zero. The form of the equation for such a line will be y= a number. In the example below, the equation would be y=5.
(Rehill, 2012).
Think of a real life situation where a graph would have no x- or y-intercept. Will what you say about the line always be true in that situation?
A situation where a graph would have…
References
Harmsworth, A.P. (2012). Plotting x-y graphs. Retrieved October 16, 2012 from GCSE.com website: http://www.gcse.com/maths/graphs3.htm
Highline Advanced Math Program. (2008). Algebraic expression. Retrieved October 16, 2012
from: http://home.avvanta.com/~math/def2.cgi?t=expression
Highline Advanced Math Program. (2008). Equation. Retrieved October 16, 2012
from: http://home.avvanta.com/~math/def2.cgi?t=equation
Math is Fun. (2012). What is a function? Retrieved October 16, 2012 from http://www.mathsisfun.com/sets/function.html
Rehill, G.S. (2012). Horizontal and vertical lines. Retrieved October 16, 2012 from Mathsteacher.com website: http://www.mathsteacher.com.au/year8/ch15_graphs/05_hor/ver.htm
linear equation and a linear inequality be solved in the same way? Explain why. What makes them different? Team B A linear equation and a linear inequality can be solved the same except for very specific scenarios: one flips the inequality sign whenever multiplying or dividing by a negative (Staples, 2012). What makes them different is that the answer will not be a single number, but a range of numbers. Stapel,