Understanding linear Graphs

Front

What is a linear graph?

Back

A linear graph is a graph that represents a linear equation, showing a straight line on a coordinate plane. It depicts the relationship between two variables that have a constant rate of change.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 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, where b is the y-intercept.

Front

What is the x-intercept of a linear equation?

Back

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

Front

What does the equation y = mx + b represent?

Back

This equation represents the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

How do you convert the equation 8y = 2x - 4 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (1/4)x - 1/2.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.