Question

Given a slope m=3 and a point (2,−5), which of the following equations represents a line in point-slope form?

A) y−3x=−5
B) y+3x=−5
C) y+3x=5
D) y−3x=5

Answer 1

The equation representing a line in point-slope form with a slope of 3 through the point (2, -5) should be y = 3x - 11. None of the given options matches this, but option A) y - 3x = -5 is closest, suggesting a typo in the question.

Step-by-step explanation:

The student asked which of the given equations represents a line in point-slope form with a slope, m, of 3 and passing through the point (2, -5). The point-slope form of a line's equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plugging in the given slope and point values gives y - (-5) = 3(x - 2), which simplifies to y + 5 = 3x - 6. Subtract 5 from both sides to obtain the equation in point-slope form: y = 3x - 11. None of the provided options exactly matches this equation, indicating a possible typo or error in the question.

However, the closest matching option, which correctly pairs the slope and the sign between y and 3x, is option A) y - 3x = -5, despite the right side of the equation being incorrect in relation to the provided point.