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 of a line given 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 represent in a linear function?

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

What is the equation of a line with a slope of 2 that passes through the point (3, 5)?

Back

The equation is y = 2x - 1.

Front

What is the graphical representation of the equation x = -4?

Back

It is a vertical line that crosses the x-axis at -4.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dashed line and shade below the line.

Front

What does the inequality symbol '≤' indicate in a linear inequality?

Back

It indicates that the values on the left side can be equal to or less than the values on the right side.

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 graph that satisfies the inequality.

Front

How do you determine if a point (x, y) is a solution to the inequality y > -rac{1}{2}x + 4?

Back

Substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the slope of the line represented by the equation y = -3x + 2?

Back

The slope is -3.