Finding Slope

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, and is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate (rise over run).

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in the y-coordinate regardless of the change in the x-coordinate.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in the x-coordinate is 0, leading to division by zero in the slope formula.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 2 units, making the line relatively steep.

Front

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

Find the slope of the line that passes through the points (1, 2) and (4, 5).

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, resulting in a line that slopes downward from left to right.

Front

If the slope of a line is -4, what is the rise and run?

Back

The rise is -4 and the run is 1, meaning for every 1 unit increase in x, y decreases by 4 units.

Front

What is the slope of the line passing through the points (-1, -1) and (2, 2)?

Back

The slope is (2 - (-1)) / (2 - (-1)) = 3 / 3 = 1.