9.5 STAAR Review Linear Key Features

A linear function is a function that graphs to a straight line. It can be expressed in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The slope of a line represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of $$b$$ in the equation $$y = mx + b$$ .

To find the x-intercept, set $$y = 0$$ in the equation of the line and solve for $$x$$ .

An x-intercept of -5 indicates that the line crosses the x-axis at the point (-5, 0). This means that when y is 0, x is -5.

The rate of change in a linear function is the same as the slope. It indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

A slope of zero indicates that the line is horizontal. This means that there is no change in y as x changes.

The equation of a horizontal line that passes through the point (a, b) is $$y = b$$ .

In a real-world context, the x-intercept often represents a point where a certain condition is met, such as the number of payments made to fully repay a loan.

The x-intercept in a loan repayment graph represents the number of monthly payments needed to repay the loan completely.