Graph y=2x+1, then choose 3 points above the line. Give the coordinates of each point and tell wether it is greater than, less than or equal to
2x + 1 at each point.
for any point that you choose above the line, the y-coordinate of that point would be greater than 2x+1
Doesn't the line go on forever, so how could you choose 3 points above it?
did you draw the line.
for any line, unless it is vertical, you can be either above or below the line.
e.g. for your y = 2x + 1
consider (6,5), below above the line.
Why?
substitute the value x = 6
then y = 2(6)+1 = 13, but the y for your point was 5
since 5 < 13, the point (6,5) is below the line.
consider (3,15)
if x=3 in the equation y = 6+1 = 7
since 15 > 7, the point (3,15) is above the line.
Draw any non-vertical line on a piece of paper. Isn't there a region above that line and a region below that line no matter you imagine that line to go ??
To graph the equation y = 2x + 1, you can start by plotting a few points. One approach is to choose some values for x, plug them into the equation, and calculate the corresponding y-values.
Let's select x = -2, 0, and 2:
For x = -2:
y = 2(-2) + 1
y = -4 + 1
y = -3
So, the first point is (-2, -3).
For x = 0:
y = 2(0) + 1
y = 0 + 1
y = 1
The second point is (0, 1).
For x = 2:
y = 2(2) + 1
y = 4 + 1
y = 5
The third point is (2, 5).
Now, let's compare the y-values obtained from the equation 2x + 1 to the y-values of these three points:
For (-2, -3):
2x + 1 = 2(-2) + 1 = -4 + 1 = -3
The y-value of the point (-2, -3) is equal to the value of 2x + 1.
For (0, 1):
2x + 1 = 2(0) + 1 = 0 + 1 = 1
Again, the y-value of the point (0, 1) is equal to the value of 2x + 1.
For (2, 5):
2x + 1 = 2(2) + 1 = 4 + 1 = 5
Once more, the y-value of the point (2, 5) is equal to the value of 2x + 1.
In each case, the y-value of the points is equal to the value of 2x + 1. Therefore, all three points lie exactly on the line y = 2x + 1.