Linear Functions Review

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation, which is given by the formula: m = (y2 - y1) / (x2 - x1).

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Use the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the slope of a line is positive?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

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

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

Back

The y-intercept is the value of y when x = 0, represented by 'b' in the equation.

Front

How can you determine if a point (x, y) is a solution to a linear equation?

Back

Substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the coordinate plane that satisfies the inequality.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

What does the term 'solution set' refer to in linear equations?

Back

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