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Find the equation of a line through (4, -2) and (6, 4).

A) y = 3x + 14
B) y = 3x - 14
C) y = -3x + 14
D) y = -3x - 14

1 Answer

7 votes

Final answer:

To find the equation of the line passing through the points (4, -2) and (6, 4), we calculated the slope to be 3 and used the point-slope form to arrive at the equation y = 3x - 14. Thus, the correct answer is B) y = 3x - 14.

Step-by-step explanation:

To find the equation of a line that passes through two points, we first calculate the slope of the line and then use one of the points to find the y-intercept. The slope (m) is determined by the change in y over the change in x, which is (y2-y1)/(x2-x1). Let's calculate the slope for the points (4, -2) and (6, 4):

m = (4 - (-2)) / (6 - 4) = 6 / 2 = 3.

Now that we have the slope, we can use the point-slope form of a line equation, y - y1 = m(x - x1), and one of the given points to find the equation. Let's use the point (4, -2):

y - (-2) = 3(x - 4)

y + 2 = 3x - 12

y = 3x - 14

The correct answer is B) y = 3x - 14.

User Nurlan Mirzayev
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