How do you graph #y-2

Question

How do you graph #y-2<3x#?

Savannah Anderson · Accepted Answer

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality. For: #x = 0# #y - 2 = 3 xx 0# #y - 2 = 0# #y - 2 + color(red)(2) = 0 + color(red)(2)# #y - 0 = 2# #y = 2# or #(0, 2)# For: #x = 1# #y - 2 = 3 xx 1# #y - 2 = 3# #y - 2 + color(red)(2) = 3 + color(red)(2)# #y - 0 = 5# #y = 5# or #(1, 5)# We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality. graph{(x^2+(y-2)^2-0.05)((x-1)^2+(y-5)^2-0.05)(y-3x-2)=0 [-16, 16, -8, 8]} Now, we can shade the right side of the line. The boundary line will be dashed because the inequality operator does not contain an "or equal to" clause. graph{(y-3x-2)<0 [-16, 16, -8, 8]}

Julia Adams · Answer

undefined To graph the inequality $ y - 2 < 3x $, follow these steps:

1. Begin by graphing the boundary line $ y - 2 = 3x $.
2. To graph the boundary line, first rewrite it in slope-intercept form: $ y = 3x + 2 $.
3. Plot the y-intercept at (0,2), and then use the slope of 3 to plot another point. For example, if you move 1 unit to the right (in the positive x-direction), you'll move 3 units up (in the positive y-direction). So, from (0,2), you'll move to (1,5).
4. Draw a dashed line through the points to represent the boundary line.

Now, to determine which side of the line to shade:
- Choose a test point not on the boundary line. A common choice is the origin (0,0).
- Substitute the coordinates of the test point into the original inequality: $ 0 - 2 < 3(0) $.
- Evaluate the inequality. If the statement is true, shade the side of the line containing the test point. If false, shade the opposite side.

Since $ -2 < 0 $ is true, shade the side of the line that contains the origin.

Your graph should show a dashed line with shading below it.

How do you graph #y-2&lt;3x#?

How do you graph #y-2<3x#?