Slope and Graphs of Lines

Front

What is the definition of slope in the context of a graph?

Back

Slope is a measure of the steepness 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 between 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 positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the slope of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope is -1/5.

Front

What is the slope of the line that passes through the points (-2, 4) and (-5, 8)?

Back

The slope is -4/3.

Front

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

Back

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

Front

Write the equation of a line with a slope of -3 and a y-intercept of -2.

Back

The equation is y = -3x - 2.

Front

If a line has a slope of 0, what does this indicate about the line?

Back

A slope of 0 indicates that the line is horizontal and does not rise or fall.

Front

If a line has an undefined slope, what does this indicate about the line?

Back

An undefined slope indicates that the line is vertical.