EOC Cateogory 2 - Describe & Graph Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope of a linear function from a graph?

Back

The slope of a linear function can be determined by selecting two points on the line, calculating the change in y (rise) and the change in x (run), and then using the formula slope (m) = rise/run.

Front

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

Back

The rate of change in a linear function represents how much the dependent variable (y) changes for a unit change in the independent variable (x). It is equivalent to the slope of the line.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the value of the dependent variable when the independent variable is zero.

Front

How can you identify a linear relationship from a table of values?

Back

A linear relationship can be identified from a table of values if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What does it mean for two variables to have a causal relationship?

Back

A causal relationship means that a change in one variable directly causes a change in another variable. This is different from correlation, where two variables may change together without one causing the other.

Front

How do you graph a linear equation in standard form?

Back

To graph a linear equation in standard form (Ax + By = C), you can find the x-intercept and y-intercept, plot these points on the graph, and then draw a straight line through them.

Front

What is the formula for converting a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What is the relationship between the slopes of two parallel lines?

Back

The slopes of two parallel lines are equal. This means that they rise and run at the same rate and will never intersect.

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.