Understanding Slope in Linear Equations

Front

What is the definition of slope in a linear equation?

Back

Slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

In the equation y=mx+b, what does the 'm' represent?

Back

The 'm' represents the slope of the line.

Front

How do you calculate the slope between 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 slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

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

Back

For every 2 units of rise, there is 1 unit of run.

Front

What is the slope of the line represented by the equation y = 4x + 12?

Back

The slope is 4.

Front

What is the slope of the line that passes through the points (2, 4) and (6, 12)?

Back

The slope is 2.