Linear Equations and Inequalities of 2 variables Spiral Rev

Front

What is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What effect does multiplying a linear function by a constant have on its graph?

Back

Multiplying a linear function by a constant greater than 1 makes the graph steeper.

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

How do you determine the slope from 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, indicating the value of y when x = 0.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

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 sign.

Front

What does it mean for a linear inequality to be in standard form?

Back

A linear inequality is in standard form when it is expressed as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Front

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

Back

The coefficients in a linear equation represent the slope and the y-intercept, determining the steepness and position of the line.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.