To determine the correct formula for the points (1,5), (2,7), (3,9), and (4,11), we need to identify the linear equation that passes through these points.
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We can observe the \(y\)-values:
- For \(x = 1\), \(y = 5\)
- For \(x = 2\), \(y = 7\)
- For \(x = 3\), \(y = 9\)
- For \(x = 4\), \(y = 11\)
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The \(y\)-values appear to increase by 2 for every increase of 1 in the \(x\)-values. This indicates a slope of 2.
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The equation of a line can be expressed in the slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
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Using the slope \(m = 2\), we can substitute one of the points to find \(b\). Let's use the point \((1, 5)\):
\[ 5 = 2(1) + b \] \[ 5 = 2 + b \] \[ b = 5 - 2 = 3 \]
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Therefore, the equation of the line fitting the points is:
\[ y = 2x + 3 \]
This matches one of the options you provided: y = 2x + 3.
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