Advanced II Patterns, Relations, Algebra, Graphing (10)

Question 1

What is the slope of a line parallel to y=mx+b

Answer 1

m

Question 2

What is the slope of a line perpendicular to y=mx+b

Answer 2

-1/m also known as the negative reciprocal so if you have m = a/b, the new slope would be m = -b/a

Question 3

How do you find the x-intercept?

Answer 3

set y=0 and solve for x

Question 4

What is domain?

Answer 4

The permissible values for the independent variable (usually x)

Question 5

What is range?

Answer 5

The permissible values for the dependent variable (usually y)

Question 6

What are all the linear equation forms?

Convert any linear equation into all three forms.

Answer 6

slope-intercept form:
y = mx+b

general form:
Ax+By+C = 0 where A must be positive and there cannot be any fractions, and the GCF must have been removed of the three terms, and where A and B cannot both be 0.

slope-point form:
comes from the equation of slope, but you sub in only one point:

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

so the slope-point form is:

y-y1 = m(x-x1)

Question 7

What is a function?

Answer 7

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

You can use the vertical line test to quickly see if a graph is a function.

Question 8

What is function notation?

Answer 8

replace the dependent variable with the notation f(independent variable) or similar so g(independent variable) also works.

When you use function notation you are stating that what you have is a function. So do not use this notation if you do not have a function.

When you sub in the independent variable to solve, function notation shows you what you subbed in since the independent variable is in the notation.

independent variable —> goes through function —> turns into dependent variable

Question 9

What does it mean to solve systems of linear equations?

(In math 10C we will only do this with two variables but it is possible to solve three variable equations if you have three equations)

Answer 9

Solve means to find the point of intersection. Set x in equation 1 equal to x in equation 2. Do the same for y. Then you will notice that there are many methods to solve for one of the variables by deliberately cancelling out the other variable. Once you have determined your first variable, you simply sub that back into one of the original equations and you will get the value of your second variable.

There are three main methods taught to solve for the first variable:
- graphing and finding the coordinates of the intersection point will allow you to find both variables simultaneously
- solving by elimination is where you add one equation to the other but manipulate the equations so as to cancel out a variable by forcing an additive inverse (for example additive inverse of 3x is -3x since when you add them together you get 0, effectively cancelling out the variable x and thus this allows you to solve for y)
- solving by substitution is rearranging one equation so that you sub in that equation into one of the variables in the other

When you use these methods you may find that there is not a point of intersection. You may find that most easily by graphing, but also if there is not a point of intersection you will notice that the substitution does not seem to be working such that you get things like 0=5 or some other false statement.

You may also find infinitely many solutions since this is where the two original equations are actually the same line. In this case you will see a truthful statement but it will not help you to get a point of intersection, such as 0=0 or 5=5. Essentially you will cancel out both variables by trying to cancel out one of them.

Otherwise you should get a value for one of your variables, and then you can proceed to find the point of intersection by using that value.