1) A linear relationship is a functional relationship between an independent and dependent variable, that is represented on a graph by a straight line

In the equation y = mx + b, each letter is a variable.

y is the dependant variable. The dependant variable is a variable whose value relies upon the independent variable. It can also be thought of as the y axis—the vertical axis on a graph.

x is the independent variable. The independent variable does not depend upon any other variable to determine its value.

m represents the rate. The rate is basically the amount of any given unit of the y axis, relative to any given unit of time (the x axis).

b symbolizes the y-intercept: the point at which the y axis is crossed. Basically, the y-intercept is where the line begins.

Let’s say the graph is representing how much it costs to buy videos from a rental store. The store charges $10.00, plus $5.00 per video.

y (the dependant variable) = The total cost of the videos
x (the independent variable) = How many videos are purchased
m (the rate) = $5.00, because it is $5.00 per video
b (the y-intercept) = $10.00, because that is how much money is charged regardless of how many videos are bought.

So if someone tried to rent 10 videos, the equation would become:

y = 5 * 10 + 10

This becomes y = $60.00

In other words, renting 10 videos costs $60.00.


2)
A. A table can be created to use to solve a problem because the pattern becomes very plain and obvious to see once the table is filled out. This makes following the pattern easier, so more and more data can be added as needed.
A graph can be used because plotting the points on the x axis and the y axis make certain aspects of the equation easier to understand—such as what the y-intercept is and where it is located.

Both methods are good for people who learn visually.

B) I often use equations to solve problems, as seen above on problem A. Equations are simple because the formula is laid out right in front of you—all you have to do is plug in the numbers where the variables are.

The equation in problem A was y = mx + b

m = $5.00
x = 10
b = $10.00

Therefore, the equation becomes y = 5 * 10 + 10

This becomes y = 50 + 10

Which ends as y = 60


By Grace T