Writing, Interpreting, & Analyzing Linear Functions

Front

What is a linear function?

Back

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.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of 3 and a y-intercept of 5?

Back

The equation is y = 3x + 5.

Front

If a linear function has a slope of -2, what does this indicate about the function's graph?

Back

A slope of -2 indicates that the graph of the function decreases as x increases, meaning for every 1 unit increase in x, y decreases by 2 units.

Front

What is the significance of the point (0, b) in a linear function?

Back

The point (0, b) represents the y-intercept of the linear function, where the line crosses the y-axis.

Front

How can you determine if a relationship is linear from a table of values?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the relationship is linear.

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 means the function is constant; the graph is a horizontal line, indicating that y does not change as x changes.

Front

Write the equation of a linear function that passes through the points (1, 2) and (3, 6).

Back

First, find the slope: m = (6 - 2) / (3 - 1) = 2. Then use point-slope form: y - 2 = 2(x - 1), which simplifies to y = 2x.