Slope and Slope-Intercept FLASHCARD

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

What does the slope-intercept form of a linear equation look like?

Back

The slope-intercept form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you find the y-intercept from the equation y = 2x + 5?

Back

The y-intercept is the value of y when x = 0. For y = 2x + 5, when x = 0, y = 5. So, the y-intercept is (0, 5).

Front

What does 'b' represent in the equation y = mx + b?

Back

'b' represents the y-intercept of the line, which is the point where the line crosses the y-axis.

Front

If a line has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = k, where k is a constant. For example, y = -4 is a horizontal line.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = -3x + 2?

Back

The slope of the line is -3.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing; as x increases, y decreases.

Front

How can you graph the equation y = 1/3x - 2?

Back

To graph y = 1/3x - 2, start at the y-intercept (0, -2) and use the slope (1/3) to find another point: from (0, -2), move up 1 unit and right 3 units to (3, -1).