Which graph represents the inequality y > -3x + 1 ?
the one where the region above the dashed line y=-3x+1 is shaded
Well, if I were to graph the inequality y > -3x + 1, I would probably draw a picture of a confused graph saying, "Wait, are you greater than me? Oh, you are! But only by a positive value, please!" So, imagine a line with a confused expression, leaning slightly above the line y = -3x + 1. That's what the graph would look like!
To graph the inequality y > -3x + 1, we need to start by graphing the equation y = -3x + 1, which is the line representing the boundary.
Step 1: Start by plotting the y-intercept, which is the point (0, 1).
Step 2: Find another point on the line by selecting any x-value and substituting it into the equation to solve for y. Let's choose x = 1. When we substitute x = 1 into the equation, we get y = -3(1) + 1 = -3 + 1 = -2. So our second point is (1, -2).
Step 3: Plot these two points on the coordinate plane and draw a straight line connecting them. This line represents the inequality y = -3x + 1.
Step 4: Since the inequality is y > -3x + 1, the solution is all the points above the line. This means we need to shade the area above the line.
The final graph will be a dashed line (since it is not included in the solution) with shading above the line.
To graph the inequality y > -3x + 1, we can start by graphing the equation y = -3x + 1, which is the boundary line for the inequality.
1. Start by plotting the y-intercept, which is the point (0, 1). This point represents the value of y when x = 0.
2. To find the x-intercept, set y = 0 in the equation -3x + 1 = 0. Solve for x:
-3x = -1
x = 1/3
So, the x-intercept is (1/3, 0).
3. Connect the y-intercept and the x-intercept with a straight line. This is the graph of y = -3x + 1.
Now, to determine which region represents the solution to the inequality y > -3x + 1, we need to determine if the inequality is greater than or equal to or strictly greater than. In this case, we have y > -3x + 1, which means the boundary line is not included in the solution.
4. Choose a point on one side of the line (not on the line itself). For simplicity, let's choose the origin (0, 0).
5. Substitute the x and y values of the chosen point into the inequality. If the inequality is true, shade the region containing that point. Otherwise, shade the region on the other side of the line.
When we substitute x = 0 and y = 0 into the inequality:
0 > -3(0) + 1
0 > 1
This inequality is false, so we shade the region on the other side of the line.
Finally, the shaded region representing the solution to the inequality y > -3x + 1 is the region above the boundary line y = -3x + 1.