Linear functions as equations (algebra/8th grade math)

Each linear function has an equation of the form y = mx + b, and conversely, an equation of that form always defines a linear function. The parameter "b" is called the initial value — it is the value of the function when the input (or independent variable) has the value zero. And m is the rate of change.

In the first example, we write an equation for a linear function when its graph and a table of values are given, and also solve two questions related to the equation.

In the second example, again we write an equation from the graph of a linear function. This time the rate of change is negative.

Lastly, we write an equation for a linear function when a few values are given in a table, and again solve a question (what will be the distance when the time is 7.5 hours).

See also

Linear Functions and the Rate of Change 2 — video lesson

Math Mammoth Grade 8 curriculum

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