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

2
3
​
that contains the point (3, 4).

y−3=
2
3
​
(x−4)

y+4=−
2
3
​
(x+3)

y−4=
2
3
​
(x−3)

None of these are correct.

1 answer

To create an equation in point-slope form, we use the formula:

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

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

Given:

  • Slope (\( m \)) = \( -\frac{2}{3} \)
  • Point (\( (x_1, y_1) \)) = \( (3, 4) \)

Substituting these values into the point-slope formula:

\[ y - 4 = -\frac{2}{3}(x - 3) \]

Now, let's compare this with the given options:

  1. \( y - 3 = \frac{2}{3}(x - 4) \)
  2. \( y + 4 = -\frac{2}{3}(x + 3) \)
  3. \( y - 4 = \frac{2}{3}(x - 3) \)
  4. None of these are correct.

The correct equation we derived is:

\[ y - 4 = -\frac{2}{3}(x - 3) \]

None of the provided options match this equation. Thus, the answer is:

None of these are correct.