Meaning of Slope, y-intercept, and x-intercept

Front

What is the meaning of the y-intercept in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of y when x is 0.

Front

What does the x-intercept represent in a graph?

Back

The x-intercept is the point where the graph crosses the x-axis, indicating the value of x when y is 0.

Front

Define slope in the context of a graph.

Back

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

Front

If a line has a slope of 4, what does this mean?

Back

A slope of 4 means that for every 1 unit increase in x, y increases by 4 units.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, 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, resulting in a downward slant of the line.

Front

How can you find the slope from two points on a line?

Back

The slope can be found using the formula: (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the term 'constant rate of change' refer to?

Back

Constant rate of change refers to a consistent change in y for a consistent change in x, represented by the slope of a linear graph.

Front

If a graph shows a candle burning down from 9 cm, what does the y-intercept represent?

Back

The y-intercept represents the initial height of the candle, which is 9 cm.