Inequalities and Systems of Equations

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 transform the equation 3x - y = 1 into slope-intercept form?

Back

To transform it, isolate y: y = 3x - 1.

Front

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents a region below or on the line y = 2x - 1.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more inequalities that share the same variables.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality; if all inequalities are satisfied, the point is a solution.

Front

What does the graph of the inequality y > -2x + 3 look like?

Back

It is a dashed line for y = -2x + 3, with the region above the line shaded.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set.

Front

What is the solution set of the system of inequalities y ≤ 2x - 1 and y > -2x + 3?

Back

The solution set is the region where both inequalities overlap.

Front

How do you graph the inequality 5x + y ≤ -1?

Back

First, graph the line 5x + y = -1 as a solid line, then shade below the line.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is non-strict (≤ or ≥).