Math 8 Flashcard (4.1-4.2)

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 (y = mx + b). It is calculated as the change in y divided by the change in x (rise/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 does an undefined slope indicate about a line?

Back

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

Front

What is the slope of a line that rises 3 units for every 4 units it runs to the right?

Back

The slope of the line is 3/4.

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that the line descends from left to right, meaning for every 2 units it moves to the right, it moves down 1 unit.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, which occurs when x = 0.

Front

Using the equation y = 2x + 3, what is the y-coordinate when x = 1?

Back

When x = 1, the y-coordinate is 5, calculated as y = 2(1) + 3.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no rise as it runs.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.

Front

What is the relationship between perpendicular lines and their slopes?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other will have a slope of -1/m.