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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:
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12 |
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11 | * (4, 11)
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10 |
|
9 |
|
8 |
|
7 | * (3, 9)
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6 |
|
5 | * (2, 7)
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4 |
|
3 | * (1, 5)
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2 |
|
1 |------------------
1 2 3 4 5
The graph is represented by a straight line that connects all the given points.