Slope and y-intercept from Graphs/Tables

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that for every 2 units you move to the right (positive x-direction), the line moves down 1 unit (negative y-direction).

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined.

Front

Given the points (2, 0) and (7, 3), calculate the slope.

Back

Slope (m) = (3 - 0) / (7 - 2) = 3/5.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises as it moves from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls as it moves from left to right.

Front

How can you find the y-intercept from a table of values?

Back

Look for the value of y when x = 0; this value is the y-intercept.