Interpreting Graphs of Linear Functions in Context

Front

What does the rate of change represent in a linear function?

Back

The rate of change indicates how much the dependent variable (y) changes for a unit change in the independent variable (x). For example, if the rate of change is 2, it means y increases by 2 for every 1 unit increase in x.

Front

How do you find the slope of a line?

Back

The slope (m) of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

Front

What does a slope of 2/3 indicate about a line?

Back

A slope of 2/3 means that for every 3 units you move to the right (increase in x), the line rises by 2 units (increase in y).

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, showing an inverse relationship between the two variables.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. For example, if one line has a slope of 2, the other must have a slope of -1/2.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope occurs in vertical lines, where the x-value does not change, resulting in a division by zero when calculating slope.

Front

How do you interpret the y-value when given an x-value in a linear function?

Back

To find the y-value for a given x-value, substitute the x-value into the linear equation and solve for y.

Front

What is the formula for a linear function in slope-intercept form?

Back

The slope-intercept form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning that the y-value remains constant regardless of the x-value.