To find the correct linear equation in slope-intercept form (y = mx + b) that passes through the points (2, -1) and (4, 5), we need to calculate the slope (m) and then the y-intercept (b).
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Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the points (2, -1) as \((x_1, y_1)\) and (4, 5) as \((x_2, y_2)\): \[ m = \frac{5 - (-1)}{4 - 2} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \]
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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. Using the point (2, -1): \[ y = mx + b \rightarrow -1 = 3(2) + b \] \[ -1 = 6 + b \rightarrow b = -1 - 6 = -7 \]
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Write the equation in slope-intercept form: \[ y = 3x - 7 \]
Now, we can match the derived equation with the given options:
A) \( y = \frac{1}{3}x - 7 \)
B) \( y = 3x - 2 \)
C) \( y = 3x - 7 \)
D) \( y = \frac{1}{3}x - 2 \)
The correct answer is:
C) y = 3x - 7