To find the equation of the line represented by the points (0, 3) and (5, -1), we can use the slope-intercept form of a line, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Find the slope (\( m \)): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 3) and (5, -1): \[ m = \frac{-1 - 3}{5 - 0} = \frac{-4}{5} = -\frac{4}{5} \]
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Find the y-intercept (\( b \)): We know from the point (0, 3) that when \( x = 0 \), \( y = 3 \). Therefore, the y-intercept \( b \) is 3.
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Write the equation: Now we can substitute the values of \( m \) and \( b \) into the slope-intercept form: \[ y = -\frac{4}{5}x + 3 \]
Now we can check which of the provided response options matches this equation:
- The corresponding response is: y = -\frac{4}{5}x + 3, which we can also read as: y is equal to negative 4 fifths x plus 3.
So the correct answer is: y is equal to negative 4 fifths x plus 3.