sket the graph of each linear inequality y<-7/3x+4
type in your expression at wolframalpha.com
It will show the graph. Play around there a while.
Yes, but the line should be dashed. I'm not sure how to make wolframalpha do that. Is there a way? Desmos.com does it nicely. Also, the thing to enter is probably y<(-7/3)x+4 (note parentheses)
To sketch the graph of the linear inequality y < (-7/3)x + 4, we can follow these steps:
Step 1: Start by drawing the graph of the related equation, y = (-7/3)x + 4. This equation represents the boundary line for the inequality.
Step 2: Plot at least two points on the line. To make it easy, we can choose x = 0 and x = 3. By substituting these x-values into the equation, we can solve for the corresponding y-values. For x = 0, y = 4, and for x = 3, y ≈ -1.67 (rounded to two decimal places).
Step 3: Connect the points on the line with a straight line.
Step 4: Choose a test point that is not on the line. The origin (0, 0) is a convenient point to choose.
Step 5: Substitute the x and y values of the test point into the original inequality (y < (-7/3)x + 4). If the inequality holds true, shade the region below the line. Otherwise, shade the region above the line.
In this case, substituting (0, 0) into the inequality, we have 0 < (-7/3)(0) + 4. Simplifying, 0 < 4. Since this is true, we shade below the line.
Step 6: Label the shaded region as the solution to the inequality.
By following these steps, you should be able to sketch the graph of the linear inequality y < (-7/3)x + 4.