Slope of a graph

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be found using the formula: 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the change in x is zero, leading to division by zero in the slope formula.

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

How can you identify the slope from the equation y = 3x + 2?

Back

In the equation y = 3x + 2, the slope (m) is 3.

Front

What is the y-intercept in the equation y = -2x + 4?

Back

In the equation y = -2x + 4, the y-intercept (b) is 4.

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

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