Certainly! Let's carefully analyze the equation step-by-step and identify the correct point and slope from the given equation [tex]\(y + 13 = -\frac{7}{2}(x - 4)\)[/tex].
### Step-by-Step Solution:
1. Identify the Form of the Equation:
The given equation is in the point-slope form, which is generally written as:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.
2. Compare the Given Equation to the Point-Slope Form:
The equation we have is:
[tex]\[
y + 13 = - \frac{7}{2}(x - 4)
\][/tex]
To match it with the standard point-slope form, we can rewrite it as:
[tex]\[
y - (-13) = -\frac{7}{2}(x - 4)
\][/tex]
By comparing,
- [tex]\( y_1 = -13 \)[/tex]
- [tex]\( x_1 = 4 \)[/tex]
- [tex]\( m = -\frac{7}{2} \)[/tex]
3. Identify the Point:
From the comparison, we see that the point [tex]\((x_1, y_1)\)[/tex] is:
[tex]\[
(4, -13)
\][/tex]
4. Identify the Slope:
The slope [tex]\(m\)[/tex] is:
[tex]\[
-\frac{7}{2}
\][/tex]
### Conclusion:
- Point: The point represented by the equation [tex]\(y + 13 = -\frac{7}{2}(x - 4)\)[/tex] is [tex]\((4, -13)\)[/tex].
- Slope: The slope of the line is [tex]\(-\frac{7}{2}\)[/tex], which is equivalent to [tex]\(-3.5\)[/tex].
The given answer in your question is incorrect because it states the slope as [tex]\(-\frac{2}{7}\)[/tex].
So the correct identification is:
- Point: [tex]\((4, -13)\)[/tex]
- Slope: [tex]\(-\frac{7}{2}\)[/tex] (or [tex]\(-3.5\)[/tex])
I hope this helps you understand how to identify the correct point and slope from the given equation in point-slope form!
