Question

Which graph accurately depicts the correct formula for the points (1, 5), (2, 7), (3, 9), and (4, 11)?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The graph of a linear equation can be represented as a straight line. To determine the equation of the line passing through the points (1, 5), (2, 7), (3, 9), and (4, 11), we need to find the slope-intercept form of the equation, which is y = mx + b.

First, we calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Taking the first two points (1, 5) and (2, 7):
m = (7 - 5) / (2 - 1) = 2 / 1 = 2

Now that we have the slope, we can find the value of the y-intercept (b) using the formula:
b = y - mx
For the point (1, 5):
b = 5 - (2 * 1) = 5 - 2 = 3

Therefore, the equation of the line passing through the points (1, 5), (2, 7), (3, 9), and (4, 11) is y = 2x + 3.

The graph of this equation is a straight line with a slope of 2 and a y-intercept of 3.

The correct graph would be a straight line passing through the points (1, 5), (2, 7), (3, 9), and (4, 11) as shown below:

|
12 |
|
11 | * (4, 11)
|
10 |
|
9 |
|
8 |
|
7 | * (3, 9)
|
6 |
|
5 | * (2, 7)
|
4 |
|
3 | * (1, 5)
|
2 |
|
1 |------------------
1 2 3 4 5

The graph is represented by a straight line that connects all the given points.