To determine which graph accurately depicts the correct formula for the given points (1, 5), (2, 7), (3, 9), and (4, 11), we first need to analyze the points to find a possible linear equation.
Let's observe the points:
- For (1, 5), the y-coordinate is 5 when x = 1.
- For (2, 7), the y-coordinate is 7 when x = 2.
- For (3, 9), the y-coordinate is 9 when x = 3.
- For (4, 11), the y-coordinate is 11 when x = 4.
Notice that as x increases by 1, the y-value increases by 2. We can derive the formula for the line:
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Identify the slope (m):
- The change in y (Δy) is 2 for every change in x (Δx) of 1, which gives us a slope of 2: \[ m = \frac{Δy}{Δx} = \frac{2}{1} = 2. \]
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Use one of the points to find the y-intercept (b):
- Using the point (1, 5) in the slope-intercept form of the line \( y = mx + b \): \[ 5 = 2(1) + b \] \[ 5 = 2 + b \] \[ b = 5 - 2 = 3. \]
So, the equation of the line for these points is: \[ y = 2x + 3. \]
Next, look for a graph that shows a line with this slope and y-intercept. Specifically, it should show a line passing through the points listed. If the graphs you described contain lines with identical slopes passing through at least two of the points given, then any graph representing such a line would be correct.
If you can visually compare the graphs provided, select the one that shows a line with a slope of 2 and passes through all four points listed.
1 answer