Q&A for How to Graph Inequalities

Since you do not have an x-squared term, you are working with a linear inequality. Turn the inequality into the equation y = x + 6. Plot the line using this equation. Since it is in the form of y = mx + b, you can tell that the y-intercept is at the point (0, 6), and that the slope is 1, or 1/1. Since it is less than OR equal to, the line should be solid. Since y is less than the line, you would shade the area below the line.

First, substitute "greater than" with "equals," which gives you x - y = 5. Then rearrange the equation to get y = x - 5. Input some values for x. If you do 1, 5, 10, you get y-values -4, 0, 5. Plot these 3 points (1,-4), (5,0) and (10,5). Then pick a point on your graph (not on the line) and put this into your starting equation. Take the point (4,2) for example. You have 4 - 2 > 5, and 2 > 5 is false. This means that the graph area on the same side of the line as point (4,2) is not in the region x - y > 5. Therefore, any point on the other side of the line should be in this region. To check, use point (8,2). 8 - 2 > 5, 6 > 5, which is true. You can then draw arrows off your line indicating the region represented by x - y > 5.

The Y-axis goes up and down; the X-axis goes left and right. Plug in x values: In the equation above, if x is 0, what is y? Plugging 0 in for x and doing the calculation gives a 1 for y. The first point, then, is (0,1). (When x is 0, y is 1.) Next, plug in 1 for x. (5 times 1) + 1 = 6. So the next point is (1,6). (When x is 1, y is 6.) Now, plug in 2 for x. (5 times 2) + 1 = 11. The next point is (2,11). Plot the points on the graph and draw a line through all of them.

Inequalities should be graphed on a number line. Solve the equation algebraically, and plot it on the line with a dot on the answer. The dot should be open, with an arrow pointing toward the left.

A graph of "no solution" would typically be two graph lines which never intersect.

Let's use two examples: The graph of y < 10 is all of the area below the horizontal line y = 10. The graph of x > 10 is all of the area to the right of the vertical line x = 10.

You’ll need to find the y-intercept (b) and the slope (m) (y = mx + b). If the inequality is < or >, the line is dashed. If the inequality is ≤ or ≥, the line is solid.

First, move the 5x to the right side where it says 15 by subtracting 5x from both sides. Now, you’re equation is 3y ≤ -5x + 15. You now divide by 3 on each side so you’re left with y ≤ -5/3 + 5. The sign did not flip sides, because we divided by 3. However, if we divided by -3, the inequality would have been ≥ greater or equal, but that’s not the case. Now we graph 3, the y-intercept, on the graph. We use our slope to calculate the line being down by 5, right by 3 and put a point there. Since the inequality includes equal, the line is solid. I hope this helps!

Since it is greater than or equal to, you should put a closed circle on -2 and then draw an arrow to the right, indicating that \( y \) can be any value -2 or greater.

Graph \( y = 3x + 2 \) on the coordinate grid and use an open circle to indicate that this line is not included.

To solve this inequality, divide both sides by -2 to get y < 3. When graphing, place an open circle on 3 and shade to the left, as less than means left and greater than means right.