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 to the horizontal change between two points on the line.

Front

How do you determine if a slope is positive, negative, zero, or undefined?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, zero if the line is horizontal, and undefined if the line is vertical.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line on a graph?

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 does an undefined slope indicate about a line on a graph?

Back

An undefined slope indicates a vertical line, where the x-values are constant and the y-values can vary.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero.

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope by selecting two points on the line, calculating the rise (vertical change) and run (horizontal change), and determining the ratio of rise to run.

Front

What is the significance of the ordered pair (x, y) in relation to a linear equation?

Back

An ordered pair (x, y) is a solution to a linear equation if it satisfies the equation when the values of x and y are substituted into it.

Front

How do you find the slope from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation -2x + 3y = 20?

Back

To find the slope, rearrange the equation to slope-intercept form (y = mx + b). The slope is 2/3.