Algebra 1 (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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

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 y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

What does a zero slope indicate?

Back

A zero slope indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value does not change, leading to a division by zero in the slope formula.

Front

Convert the equation 2x - 3y = 10 to slope-intercept form.

Back

y = (2/3)x - (10/3).

Front

Identify the slope and y-intercept of the function y = 4x + 5.

Back

Slope: 4, Y-intercept: (0, 5).