Question

Question
Write an equation in point-slope form for the given line.



Choose the correct answer below.

(1 point)
Responses

y−4=13(x−3)
𝑦
−
4
=
1
3
(
𝑥
−
3
)
y minus 4 is equal to 1 third times open paren x minus 3 close paren

y−3=−13(x−4)
𝑦
−
3
=
−
1
3
(
𝑥
−
4
)
y minus 3 is equal to negative 1 third times open paren x minus 4 close paren

y−3=13(x−4)
𝑦
−
3
=
1
3
(
𝑥
−
4
)
y minus 3 is equal to 1 third times open paren x minus 4 close paren

y−4=−13(x−3)

Answer 1

To write an equation in point-slope form, we use the format:

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

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

From the options provided, we need to identify the correct point and slope.

1. **If we have a point (3, 4) and a slope of \(\frac{1}{3}\)**:
\[
y - 4 = \frac{1}{3}(x - 3)
\]

2. **If we have a point (4, 3) and a slope of \(-\frac{1}{3}\)**:
\[
y - 3 = -\frac{1}{3}(x - 4)
\]

3. **If we have a point (4, 3) and a slope of \(\frac{1}{3}\)**:
\[
y - 3 = \frac{1}{3}(x - 4)
\]

4. **If we have a point (3, 4) and a slope of \(-\frac{1}{3}\)**:
\[
y - 4 = -\frac{1}{3}(x - 3)
\]

Based on this analysis, you should select the equation that matches the given point and slope. Without specific values for the point and slope, we can't definitively say which option is correct.

However, if you have the point and slope provided in the question, choose the corresponding equation based on the analysis above.