Writing Linear Inequalities from Graphs

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which are the points that satisfy the inequality.

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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 <).

Front

How do you write a linear inequality from a graph?

Back

To write a linear inequality from a graph, identify the slope and y-intercept of the line, determine the direction of the inequality based on the shading, and use the appropriate inequality symbol.

Front

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

Back

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

Front

What does the shading in the graph of a linear inequality indicate?

Back

The shading indicates the region of the graph that contains all the solutions to the inequality.

Front

How can you tell which side of the line to shade in a linear inequality?

Back

You can test a point not on the line (often (0,0) if it's not on the line) to see if it satisfies the inequality. If it does, shade that side; if not, shade the opposite side.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are real numbers.

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.