Create a table 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.

1 answer

To create a table that meets both conditions, we need to find the x and y values that satisfy the given equation. The equation of a straight line is represented as y = mx + b, where m is the slope and b is the y-intercept.

Given that the y-intercept is 5, we know that at the point where the line crosses the y-axis (when x = 0), the y-value will be 5. In other words, when x = 0, y = 5.

To determine the slope of the line, we need to find the change in y divided by the change in x between any two points on the line. Since we only have the y-intercept given, we can choose any x-value to find the slope. Let's say we choose x = 1, and we are given that the y-intercept is 5.

When x = 0, y = 5, and when x = 1, we can substitute these values into the equation y = mx + b:

5 = 1*1 + b

Simplifying the equation:

5 = 3 + b

Subtracting 3 from both sides:

2 = b

Therefore, the equation of the line is y = 3x + 2.

Using this equation, we can create a table with different x-values and calculate the corresponding y-values:

| x | y |
|-------|------|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| 3 | 14 |
| 4 | 17 |
| 5 | 20 |

Now, we have a table that meets the given conditions, where the y-intercept is 5 and the slope is 3.