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Select the equation for the line that passes through (2, 5) and (6, 7).

Multiple choice question.
A) y + 5x − 2=12
B) y + 5x + 2=12
C) y − 5x − 2=12
D) y − 5x + 2=12

User Miroo
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1 Answer

2 votes

Final answer:

To find the equation of the linear line that passes through the given points, calculate the slope and then use one of the points to find the equation using point-slope form. The correct equation based on the calculations is x - 2y = -8, which does not match any of the provided multiple-choice options, indicating a potential error in the question.

Step-by-step explanation:

To find the equation of the line that passes through the points (2, 5) and (6, 7), we first need to determine its slope (m). The slope of a line through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Substituting our points into this formula, we get m = (7 - 5) / (6 - 2) = 2 / 4 = 1/2.

We then use the point-slope form of a linear equation, y - y1 = m(x - x1), and substitute one of the points and the slope to find the equation. Let's use the point (2, 5): y - 5 = 1/2(x - 2). Now, we'll simplify this to the slope-intercept form, y = mx + b. Multiplying both sides by 2 and then simplifying gives us 2y - 10 = x - 2, and then moving terms around yields x - 2y = -8.

By looking at the multiple choice options, we need to express this equation in the form y = mx + b or something that can be rearranged to that form. The correct equation must be equivalent to x - 2y = -8. The answer is not listed in the provided options; therefore, there could be an error in the question or the answer choices.

User Mike Chiu
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7.8k points

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