The process of representing the solution set of an inequality on a coordinate plane by drawing the boundary line (solid for ≤/≥, dashed for </>) and shading the half-plane that contains all points satisfying the inequality.
Use boundary lines and shading to show where conditions are true.
Showing a random 20 of 50 problems.
Example 1
medium
Where is the solution region of the system y≥0 and x≥0?Solid x-axis (y ≥ 0) and y-axis (x ≥ 0); solution region is the first quadrant including axes
Example 2
easy
Graph x>2 on a number line.Open circle at 2 (strict inequality), shaded ray to the right
Example 3
easy
When graphing y<2x+1, is the boundary line solid or dashed?Boundary line y
Example 4
hard
For the system {x≥0,y≥0,x+y≤4}, what is the area of the solution region?
Example 5
medium
For 2x+y≤4, rewrite in y-form and state the shading side (test (0,0)).Solid line y = −2x + 4; origin satisfies 0 ≤ 4, so shade below (origin side)
Example 6
easy
Is the line dashed or solid for 2x+3y>6?
Example 7
easy
What kind of line do you draw for x≥0 on the coordinate plane?Solid vertical boundary at x = 0 (the y-axis); shade the right half-plane
Example 8
medium
Graph ∣x∣≤2 on the coordinate plane — describe the region.Solid vertical boundaries at x = −2 and x = 2; solution is the strip −2 ≤ x ≤ 2
Example 9
medium
Find the slope and y-intercept of the boundary of 4x+2y<8.
Example 10
medium
Test (1,1) for the system y<x+2 and y>x−1. Is it in the solution region?Point (1,1) is between the two parallel lines and satisfies both y < x+2 and y > x−1
Example 11
easy
Graph y>−2 on the coordinate plane.
Example 12
hard
A produce stand makes $2 per pound on apples and $3 per pound on pears. The owner can ship at most 50 pounds total and must ship at least 10 pounds of apples. Write the system of inequalities.
Example 13
medium
Which inequality has the point (3,2) on its solid boundary?
Example 14
hard
Graph y≤∣x∣−1 on the coordinate plane.
Example 15
hard
How many integer points (x,y) satisfy x≥0, y≥0, and x+y≤3?
Example 16
hard
For which value of k does the line y=2x+k pass through (3,4) as the solid boundary of an inequality containing (0,0)?
Example 17
hard
Write a system of inequalities whose solution is the triangle with vertices (0,0), (4,0), and (0,3).
Example 18
medium
Find the inequality whose graph is a dashed line through (0,2) and (1,5), shaded below.
Example 19
easy
Is (2,5) a solution of y>2x?Point (2,5) lies above y = 2x since 5 > 4; it is in the solution region
Example 20
easy
Graph x≤−1 on a number line.Closed circle at −1 (inclusive inequality), shaded ray to the left