Question

Use point-slope form to write an equation of the line with the given slope that passes through the given point:

Slope (m) = 2/3, Point (-3, 4/2)
A) y - 0 = (2/3)(x + 2)
B) y - 2 = (2/3)(x + 0)
C) y + 2 = (2/3)(x - 0)
D) y - 0 = (2/3)(x - 2)

Answer 1

Using a point-slope form, the correct equation of the line with the given slope 2/3 that passes through the given point (-3, 2) should be y - 2 = (2/3)(x + 3). None of the given options match this equation, indicating a possible typo in the answer choices.

Step-by-step explanation:

To write the equation of a line in point-slope form, we use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. The given slope (m) is 2/3 and the given point is (-3, 4/2), which simplifies to (-3, 2). Plugging these values into the point-slope formula, we get:

y - 2 = (2/3)(x + 3)

Now, we must find which answer choice matches our equation:

A) y - 0 = (2/3)(x + 2)

B) y - 2 = (2/3)(x + 0)

C) y + 2 = (2/3)(x - 0)

D) y - 0 = (2/3)(x - 2)

Option B closely resembles our equation but has x + 0 instead of x + 3. Therefore, none of the options presented is correct. There may have been a typo in the answer choices provided, as the correct point-slope form of the equation should reflect the given slope and point.