Identifying Slope From a Graph

Front

What is the definition of slope in a graph?

Back

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

Front

How do you calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

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 vertical change as you move along the line.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no horizontal change as you move along the line.

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope of the line is 4/1 or simply 4.

Front

If a line has a slope of -5/3, what does this indicate about its direction?

Back

A slope of -5/3 indicates that the line descends from left to right, meaning it goes down 5 units for every 3 units it runs to the right.

Front

What is the slope of a line that rises 1 unit for every 2 units it runs?

Back

The slope of the line is 1/2.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope from a graph, select two points on the line, count the vertical change (rise) and the horizontal change (run), and then use the slope formula (rise/run).

Front

What is the relationship between the slope of a line and its angle of inclination?

Back

The slope of a line is related to its angle of inclination; a steeper slope corresponds to a larger angle, while a shallower slope corresponds to a smaller angle.

Front

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

Back

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