Flashcard - Writing Equation of a line, graphing linear inequalities

Front

What is the formula for 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

How do you calculate 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 represent in a linear equation?

Back

The y-intercept represents the point where the line crosses the y-axis, which is the value of y when x = 0.

Front

How can you determine the y-intercept from the equation of a line in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

You can write the equation in slope-intercept form: y = mx + b, substituting m for the slope and b for the y-intercept.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you convert the general form of a linear equation to slope-intercept form?

Back

To convert Ax + By + C = 0 to slope-intercept form, solve for y: y = (-A/B)x - (C/B).

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, such as 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.