Graphing Linear Equations and Inequalities from Standard Form

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope is represented by the coefficient m.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value b in the slope-intercept form.

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 can 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.

Front

What is an inequality in the context of linear equations?

Back

An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or equal to the other.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality sign.

Front

What does the x-intercept represent in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, represented by the coordinates (x, 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 is the difference between a solid line and a dashed line when graphing inequalities?

Back

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