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Given that a line passes through the points (7, 5) and (11, -7), write the equation of the line in standard form. Which of the following options is the correct equation?

A. 3x - y = 8
B. 3x + y = 16
C. 3x - y = 16
D. 3x + y = 26"

User Kevin Horn
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1 Answer

2 votes

Final answer:

To determine the standard form equation of a line passing through the points (7, 5) and (11, -7), you calculate the slope, use it to find the y-intercept, and then rearrange the equation. The correct standard form equation is 3x + y = 26.

Step-by-step explanation:

To find the equation of the line in standard form that passes through the points (7, 5) and (11, -7), first, we need to calculate the slope (m) of the line using the slope formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given points into the formula, we get:

m = (-7 - 5) / (11 - 7) = -12 / 4 = -3

With the slope known, we choose one of the points to find the y-intercept (b) using the formula for a line, y = mx + b. Let's use the point (7, 5):

5 = (-3)(7) + b

b = 5 + 21 = 26

The equation of the line in slope-intercept form is:

y = -3x + 26

To convert this to standard form, where Ax + By = C, we rearrange the terms:

3x + y = 26

This matches option D from the given choices. Hence, the correct equation in standard form of the line passing through the points (7, 5) and (11, -7) is 3x + y = 26.

User Gbenga
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