Slope and Y-Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope (m) of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you calculate the slope between 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 definition of the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How can you find the y-intercept from the slope-intercept form of a linear equation?

Back

In the slope-intercept form, y = mx + b, the y-intercept (b) is the constant term.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero when calculating the slope.

Front

How can you determine the slope from a graph of a linear equation?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and use the formula m = rise/run.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they will never intersect.