Create an equation in point-slope form to represent a line with a slope of

Question

3
2
​
that contains the point (−2, −3).

y+2=
3
2
​
(x+3)

y−3=
3
2
​
(x−2)

y+3=
3
2
​
(x+2)

None of these are correct.

Answer 1

To create an equation in point-slope form for a line with a given slope and a point, you can use the formula:

\[ y - y_1 = m(x - x_1) \]

where \( m \) is the slope and \((x_1, y_1)\) is the point the line passes through.

In this case, the slope \( m \) is \(\frac{3}{2}\) and the point is \((-2, -3)\). Plugging in these values, we have:

\[ y - (-3) = \frac{3}{2}(x - (-2)) \]

This simplifies to:

\[ y + 3 = \frac{3}{2}(x + 2) \]

So, the correct equation in point-slope form is:

\[ y + 3 = \frac{3}{2}(x + 2) \]

Thus, the correct option is:

\( y + 3 = \frac{3}{2}(x + 2) \).

This means the answer to your question is:

\[ y + 3 = \frac{3}{2}(x + 2) \]

You can verify that the other options are incorrect based on the point and slope given.