To find the equation of the line represented by the points (4, 17) and (1, 8), we can use the point-slope form of a linear equation or find the slope and y-intercept directly.
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Calculate the slope (m): The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, 8) and (4, 17): \[ m = \frac{17 - 8}{4 - 1} = \frac{9}{3} = 3 \]
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Use the slope to find the y-intercept (b): We can use one of the points and the slope to find the y-intercept \( b \) using the equation: \[ y = mx + b \] Using the point (1, 8): \[ 8 = 3(1) + b \] \[ 8 = 3 + b \] \[ b = 8 - 3 = 5 \]
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Write the equation: Now, substituting the slope and y-intercept into the y = mx + b format, we get: \[ y = 3x + 5 \]
Thus, the completed equation is: \[ y = 3x + 5 \]
Therefore, the answer is: 3 and 5.