A.3C: Key Features of Graphs - Slope, Intercepts, and Zeros

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

What are the four types of slope?

Back

1. Positive Slope: Line rises from left to right. 2. Negative Slope: Line falls from left to right. 3. Zero Slope: Horizontal line, no rise. 4. Undefined Slope: Vertical line, no run.

Front

How do you find the y-intercept of a line?

Back

The y-intercept is found by determining the point where the line crosses the y-axis, which occurs when x = 0.

Front

What does the ordered pair (0, b) represent?

Back

It represents the y-intercept of a line, where 'b' is the value of y when x is 0.

Front

What is the formula for calculating slope (m)?

Back

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal and does not rise or fall.

Front

What does a negative slope indicate about a line?

Back

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

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, occurring when y = 0.

Front

How can you determine the slope from a graph?

Back

By selecting two points on the line, calculating the rise (change in y) and run (change in x), and using the slope formula.

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 5.