Slope using multiple representations

Front

What is the slope-intercept equation?

Back

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

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you find 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 an undefined slope?

Back

An undefined slope occurs in a vertical line where the change in x is zero, making the slope calculation impossible.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

How do you convert a slope-intercept equation to standard form?

Back

To convert y = mx + b to standard form Ax + By = C, rearrange the equation to isolate x and y on one side.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line, calculating the rise (change in y) over the run (change in x).