Linear Functions and Equations

SAT Questions that focus on Linear Functions and Equations require knowledge of the following topics.

A linear function is any function that can be rearranged in the form: f(x) = ax + b, where coeficients "a" and "b" are real numbers.

The graph of a linear function is a straight line.

For example, f(x) = x + 3 (blue line in the graph below) and f(x) = x + 1 (red line):

Coeficient "b" (in f(x) = ax + b) is called the intercept of the line, because it is where the line crosses the y-axis (the line crosses the x-axis in "-b/a").

Coeficient "a" (in f(x) = ax + b) is called the slope of the line. a=1 in both f(x) = x + 3 and f(x) = x + 1. That is why both the blue and the red lines in the previous graph have the same slope (1).

The greater the value of "a" is, the greater the slope of the line. When a = 2, for example, as "x" increases 1, f(x) increases 2. When a = 5, as "x" increases 1, f(x) increases 5. In the graph below, for example, the blue line represents f(x) = 2x + 1 and the red line represents f(x) = 5x + 1:

Note that the two lines cross the y-axis in point 1, because in both equations coeficient "b" equals 1.

In all of the previous examples the slopes of the equations ("a") are greater than zero. That's why all the lines in the graphs are ascending. When "a" is lower than zero, the line is descending. In the graph below, for example, the red line represents f(x) = -x + 3:

Solved SAT Practice Tests

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SAT Practice Tests - Linear Functions and Equations

Additional Practice Tests - Linear Functions and Equations