To determine the equation of the line represented by the points (1, 60) and (7, 140), we need to find the slope (m) and the y-intercept (b) of the line using the slope-intercept form \( y = mx + b \).
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Calculate the slope (m):
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the points \((1, 60)\) and \((7, 140)\): \[ m = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3} \]
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Use the slope to find the y-intercept (b):
We can use the slope-intercept form \( y = mx + b \) and take one of the points to find b. Using the point (1, 60): \[ 60 = \frac{40}{3}(1) + b \]
Solving for b: \[ 60 = \frac{40}{3} + b \] \[ b = 60 - \frac{40}{3} \] To subtract, convert 60 into thirds: \[ 60 = \frac{180}{3} \] So, \[ b = \frac{180}{3} - \frac{40}{3} = \frac{140}{3} \]
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Write the equation of the line:
Now that we have both m and b, the equation is: \[ y = \frac{40}{3}x + \frac{140}{3} \]
This matches with the response \( y = \frac{40}{3}x + \frac{140}{3} \).
Thus, the correct answer is: y = \(\frac{40}{3}\)x + \(\frac{140}{3}\).
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