*linear function*represents a relationship between two variables in which one variable influences the other.

In a linear function, *x* is usually considered to be the independent variable and *y* to be the dependent variable (*x* influences *y*). The independent variable (*x*) runs horizontally, while the dependent variable (*y*) runs vertically. The minimum number of points you need to construct a line is two.

The common difference of the points that describes both the steepness and direction of the line is called the *slope*. This is also referred to as the *ratio* of the rate of change in the dependent variable to the rate of change in the independent variable. The letter associated with slope is *m*; if *m* is positive, then the line rises to the right, and if *m* is negative, then the line falls to the right. To determine the slope of a line, you need two points: (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}). Then substitute into the formula:

*Slope-intercept* is the most commonly used formula to represent a linear function. Just as the name implies, this formula tells you the slope (*m*) of the line as well as the *y*-intercept (*b*). Recall that the *y*-intercept is the point at which the graph crosses the *y*-axis.

Slope-intercept form: y = mx + b (m is the slope and b is the y-intercept)

## Practice questions

## Answers and explanations

**The correct answer is Choice (A).**Because you're looking for a line*perpendicular*to the given line, the new equation would have a negative reciprocal of the given slope: so the new slope is*m*= 2. Because Choice (A) is the only equation with that slope, it is the correct answer. Choice (C) represents a line parallel to the given line, while Choices (B) and (D) have slopes that have no specific relationship with the given slope.**The correct answer is Choice (A).**Because you're looking for a line parallel to the given line, the new equation would have the same slope:*m*= –3. Because Choice (A) is the only equation with that slope, it's the correct answer. Choice (C) represents a line perpendicular to the given line, while Choices (B) and (D) have slopes that have no specific relationship with the given slope.