To find the equation of the line that passes through the points \( (8, -7) \) and \( (-7, 8) \), we can follow these steps:
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Calculate the slope (m) of the line using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (8, -7) \) and \( (x_2, y_2) = (-7, 8) \).
Substitute the values into the formula: \[ m = \frac{8 - (-7)}{-7 - 8} = \frac{8 + 7}{-15} = \frac{15}{-15} = -1 \]
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Use the point-slope form of the line to find the equation of the line. The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] We can use one of the points, say \( (8, -7) \): \[ y - (-7) = -1(x - 8) \] Simplifying the equation: \[ y + 7 = -1(x - 8) \] \[ y + 7 = -x + 8 \] \[ y = -x + 1 \]
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Convert to slope-intercept form: The equation of the line in slope-intercept form is: \[ y = -x + 1 \]
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Graph the line: To graph \( y = -x + 1 \):
- Start with the y-intercept (0, 1).
- The slope is -1, meaning for every 1 unit to the right, the line goes down 1 unit.
Now, you can plot the points \( (8, -7) \) and \( (-7, 8) \), and draw a straight line through them, following the slope.
Thus, the equation of the line is: \[ \boxed{y = -x + 1} \]