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, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is slope calculated using two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down, and there is no horizontal change.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning it does not rise or fall as it moves from left to right.

Front

What is the slope of a line that rises 3 units for every 1 unit it runs?

Back

The slope of the line is 3, calculated as rise/run = 3/1.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning it falls as it moves horizontally.

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

How do 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 calculate the slope as rise/run.

Front

What is 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 is the significance of the y-intercept in a linear equation?

Back

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