check for understanding graphing line with slope and point

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness of a line, calculated as the rise (change in y) over the run (change in x).

Front

How do you find the slope of a line given 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 x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

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.

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) in the slope-intercept form.

Front

How do you graph a line given a slope and a point?

Back

Start at the given point, use the slope to determine the rise and run, and plot another point. Draw a line through the points.

Front

What is the significance of the point (0, b) in a linear equation?

Back

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

Front

If a line has a slope of 2/3, what does this mean in terms of rise and run?

Back

For every 2 units the line rises, it runs 3 units to the right.

Front

How can you determine if a graph has a slope of -1?

Back

If the line descends at a 45-degree angle from left to right, it has a slope of -1.