Slope-Intercept Form

Front

What is the slope-intercept form of a linear equation?

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 slope of a line given 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 the slope of a line represent?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it does not have a defined rise over run.

Front

What is the y-intercept in the slope-intercept form?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line falls as it moves from left to right, meaning for every 1 unit increase in x, y decreases by 2 units.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various rates of change in real-world contexts, such as speed, cost per item, or growth rates.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.