Identifying and Interpreting Slope and y-intercept

Front

What is the slope of a line?

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/run).

Front

How do you find the slope from 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 does the y-intercept represent in a real-world context?

Back

In a real-world context, the y-intercept often represents the initial value or starting point of a situation.

Front

If a line has a slope of 4/1, what does this mean?

Back

This means that for every 1 unit increase in x, the y-value increases by 4 units.

Front

If a line has a slope of -5/7, what does this mean?

Back

This means that for every 7 units increase in x, the y-value decreases by 5 units.

Front

What is the formula for the slope-intercept form of a line?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify the slope from a graph?

Back

You can identify the slope by selecting two points on the line, calculating the rise (change in y) and run (change in x), and then dividing rise by run.