Page 193 - ABCTE Study Guide_Neat

C y = 4x - 2

D y = 3x - 1

Answer

The correct answer is D. This is the only rule that works each time. On a multiple-choice test, you can
always work backwards from the answers rather than having to actually figure out the rule on your own.

Review

• An independent variable (x) is the variable that changes; the dependent
variable (y) is affected by the change in the independent variable.
• A relation is any set of ordered pairs.
• A function is a special kind of relation. In a function, there can only be one x-value for
each y-value. There can be duplicate y-values but not duplicate x-values in a function.
• When there is one and only one y-value for each x-value (no duplicates in y), it is called
a one-to-one function.
• You can determine if a relation is a function by looking at its table of values or by using
the vertical-line test on the graph of the function.
• A function rule is an equation that describes a function, and it may use the function
notation f(x).
• In an inverse function, the x-values (domain) and y-values (range) are switched.
• A linear function produces the graph of a straight line, which you can make from a
table of values or from a linear-function rule.
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• In a linear-function rule, the highest power of x is one. There are no x or x in a linear
function.
• Linear functions have a constant rate of change (slope), which is the change
in y divided by the change in x. It can be represented as Δy/Δx.
• Constant rate of change can be determined from the graph of a function or a table of
values.
• Writing a linear-function rule from a table of values can be done with a combination of
mental math and by using the rate of change to figure out how to get from x (input)
to y (output).

Linear Equations

Lesson Objective

In the upcoming pages, we'll cover linear equation, and look more closely at slope. We'll also review how to
graph linear equations and see how those graphs compare with graphical representations of linear inequalities.

Previously Covered

• In previous sections, we discussed the difference between the independent variable and
the dependent variable.
• We also covered functions, function rules, and introduced the concept of slope.

The Parts of a Linear Equation