8.4C: 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 is calculated as the rise over run, or the change in y divided by the change in x.

Front

How is the y-intercept defined in a linear equation?

Back

The y-intercept (b) of a linear equation is the value of y when x is equal to zero. It represents the point where the line crosses the y-axis.

Front

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

Back

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

Front

How do you calculate the slope from two points on a graph?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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, showing a direct relationship.

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, showing an inverse relationship.

Front

What is the significance of a slope of zero in a linear equation?

Back

A slope of zero indicates a horizontal line, meaning that the dependent variable (y) does not change as the independent variable (x) changes.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope occurs in a vertical line, indicating that the x-value does not change while the y-value can vary, leading to division by zero in the slope formula.

Front

How can you determine the slope and y-intercept from a graph?

Back

To determine the slope from a graph, identify two points on the line and use the slope formula. The y-intercept is the point where the line crosses the y-axis.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line represents the rate of change of the dependent variable with respect to the independent variable, indicating how much y changes for a unit change in x.