Create a table that has 5 points that meets both of the following conditions: the y-intercept is 5 the slope is 3 Explain how you know that the y-intercept is 5. Explain how you know that the slope is 3.
To create a table that meets both conditions, the y-intercept must be 5 and the slope must be 3. The y-intercept represents the point where the graph intersects the y-axis which occurs when x=0. In this case, the y-intercept is given as 5, which means the point on the graph when x=0 is (0, 5).
To find the slope, we need at least two points on the graph. We can choose any two points on the line and use the slope formula to calculate it. Let's choose two points, (0, 5) and (1, 8).
The slope formula is:
slope = (y2 - y1) / (x2 - x1)
Using our chosen points:
slope = (8 - 5) / (1 - 0) = 3 / 1 = 3
This confirms that the slope between any two points on the line is 3.
Now, we can create a table by selecting three more values for x (different from 0 and 1) and calculating the corresponding y-values using the equation: y = 3x + 5.
Let's choose x = -1, 2, and 4.
When x = -1:
y = 3(-1) + 5 = -3 + 5 = 2
So, the point is (-1, 2).
When x = 2:
y = 3(2) + 5 = 6 + 5 = 11
So, the point is (2, 11).
When x = 4:
y = 3(4) + 5 = 12 + 5 = 17
So, the point is (4, 17).
Combining all the points, the table is:
| x | y |
---------
| 0 | 5 |
| 1 | 8 |
| -1 | 2 |
| 2 | 11 |
| 4 | 17 |
These points satisfy both conditions, with a y-intercept of 5 and a slope of 3.