Graphing Linear Equations

Front

What is the definition of slope in a linear equation?

Back

The slope 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 do you identify the slope from the equation of a line in slope-intercept form?

Back

In the slope-intercept form of a linear equation, y = mx + b, the slope (m) is the coefficient of x.

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

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

How can you determine if a slope is zero?

Back

A slope is zero when the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form, start at the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot additional points.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the relationship between perpendicular lines in terms of slope?

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.