Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph the inequality y ≤ 3/5x + 1?

Back

1. Graph the line y = 3/5x + 1 as a solid line. 2. Shade below the line to represent all points where y is less than or equal to the line.

Front

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

Back

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

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What does the inequality 2x - 5y ≤ -10 represent graphically?

Back

It represents a region on the coordinate plane that includes all points (x, y) that satisfy the inequality, with a boundary line where 2x - 5y = -10.

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

How do you convert the inequality 2x + 5y ≥ 10 into slope-intercept form?

Back

Rearranging gives y ≥ -2/5x + 2. This shows the slope is -2/5 and the y-intercept is 2.

Front

What does the graph of y ≥ -5/4 + 3 look like?

Back

It has a solid line with a slope of -5/4 and a y-intercept of 3, shading above the line.

Front

What is the significance of the y-intercept in graphing inequalities?

Back

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