Understanding linear Graphs

Front

What is the definition of slope in a linear graph?

Back

The slope is a measure of the steepness of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a linear graph?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that y does not change as x changes.

Front

What does an undefined slope mean?

Back

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

Front

What is the y-intercept of a linear equation?

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

How can you find the y-intercept from the equation 8y = 2x - 4?

Back

Rearranging to slope-intercept form gives y = (1/4)x - 1/2, so the y-intercept is (0, -1/2).

Front

How can you find the y-intercept from the equation y = 5x + 4?

Back

In slope-intercept form, the y-intercept is directly given as (0, 4).

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.