Directions are that i have to solve the equation and graph it using words.I have to include whether itis a solid or dotted line and which way the shading is.
Problem: -2x+3y<-6
dotted line. There is no equals in the problem. Which way for shading...
solve for y
y<2/3 x -2 (check this)
so if y is less than the line 2/3 x -2, it is below (below is less than).
To solve the equation -2x + 3y < -6, we need to rearrange it to isolate y.
The first step is to subtract -2x from both sides of the inequality:
-2x + 3y - (-2x) < -6 - (-2x)
This simplifies to:
3y < -6 + 2x
Next, we divide both sides of the inequality by 3 to solve for y:
(3y)/3 < (-6 + 2x)/3
Simplifying further:
y < (2/3)x - 2
So the equation of the line is y = (2/3)x - 2.
Since there is no "equal to" sign in the original inequality, the graph of the equation will have a dotted line.
To determine which way to shade, we can choose a test point, such as (0,0). Substituting these values into the inequality, we get:
0 < (2/3)(0) - 2
0 < -2
Since 0 is not less than -2, the test point does not satisfy the inequality.
Therefore, we shade the region below the dotted line to represent the solution to the inequality -2x + 3y < -6.