8.4A Slope Triangles

Front

What is a slope triangle?

Back

A slope triangle is a right triangle used to represent the slope of a line on a graph, where the vertical leg represents the rise and the horizontal leg represents the run.

Front

How do you calculate the slope of a line?

Back

The slope (m) is calculated using the formula m = rise/run, where 'rise' is the change in the y-coordinates and 'run' is the change in the x-coordinates between two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

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

Front

How can slope triangles help in graphing linear equations?

Back

Slope triangles help visualize the steepness of a line and the relationship between the x and y coordinates, making it easier to graph linear equations.

Front

What is the relationship between slope and steepness?

Back

The greater the absolute value of the slope, the steeper the line. A slope of 1 is less steep than a slope of 3.

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit you move horizontally (run), the line rises 2 units vertically.

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.