Finding Slopes Using Graphs and Coordinate Points

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, 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 using two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value decreases, meaning the line falls from left to right.

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

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0.

Front

If a line has a slope of 3/4, what does this mean in terms of rise and run?

Back

For every 4 units moved horizontally (run), the line rises 3 units (rise).

Front

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

Back

m = (y2 - y1) / (x2 - x1) where m is the slope.

Front

What is the slope of the line represented by the points (2, 3) and (5, 7)?

Back

Slope = (7 - 3) / (5 - 2) = 4/3.