Graphing Linear Inequalities (standard form & y=mx+b)

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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 to isolate it on one side of the equation.

Front

What does the slope-intercept form of a linear equation represent?

Back

The slope-intercept form, y = mx + b, represents a line where m is the slope and b is the y-intercept.

Front

What is the meaning of the inequality symbol '≥'?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Then shade the appropriate region based on the inequality.

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the point where the graph of the equation crosses the x-axis, indicating the value of x when y = 0.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What does the inequality symbol '<' represent?

Back

The symbol '<' means 'less than', indicating that the value on the left is smaller than the value on the right.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (for '≥' or '≤'), while a dashed line indicates that points on the line are not included (for '>' or '<').

Front

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

Back

The slope of the line is 2, which indicates that for every unit increase in x, y increases by 2 units.