Linear Functions & Inequalities

Front

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

Back

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

Front

How do you find the slope (m) 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 the y-intercept (b) represent in the equation y = mx + b?

Back

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

Front

What is the meaning of a positive slope in a linear function?

Back

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

Front

What does a negative slope indicate about a linear function?

Back

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

Front

What is the significance of an undefined slope?

Back

An undefined slope occurs in vertical lines, where x remains constant and y can vary, indicating no change in x.

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, expressed in forms like y < mx + b or y ≥ mx + b.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

Front

What does the term 'solution set' mean in the context of linear inequalities?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.