Question

Choose the graph that has the point (-1, -2) AND a slope of 1/3
.(1 point)
Responses

Answer 1

To determine the graph that features the point (-1, -2) and a slope of \( \frac{1}{3} \), we can use the point-slope form of a linear equation. The point-slope form is given by:

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

In this equation:
- \( (x_1, y_1) \) is the point \((-1, -2)\),
- \( m \) is the slope, which is \( \frac{1}{3} \).

Substituting in the values, we get:

\[
y - (-2) = \frac{1}{3}(x - (-1))
\]

Simplifying this gives:

\[
y + 2 = \frac{1}{3}(x + 1)
\]

Which leads to:

\[
y + 2 = \frac{1}{3}x + \frac{1}{3}
\]

Subtracting 2 from both sides:

\[
y = \frac{1}{3}x + \frac{1}{3} - 2
\]

\[
y = \frac{1}{3}x - \frac{5}{3}
\]

Now that we have the equation of the line, we can check the graph you have for the following characteristics:
1. It must pass through the point (-1, -2).
2. The slope of the line must be \( \frac{1}{3} \).

If you provide the graphs or their specifics, I can help you identify the correct one.