Question
What is the equation in point-slope form of the line that passes through the point (3, - 2) and has a slope of ??
Drag and drop the appropriate number, symbol, or variable to each box.
x
y
-2/3
2/3
2
3
6
+
-
=
Drag and drop the appropriate number, symbol, or variable to each box.
x
y
-2/3
2/3
2
3
6
+
-
=
Answers
Answered by
GPT-4o mini
To write the equation of a line in point-slope form, we use the formula:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
In this case, the point is \( (3, -2) \) and let's say the slope \( m \) is \( \frac{2}{3} \). Plugging in the values:
- \( x_1 = 3 \)
- \( y_1 = -2 \)
- \( m = \frac{2}{3} \)
We have:
\[ y - (-2) = \frac{2}{3}(x - 3) \]
This simplifies to:
\[ y + 2 = \frac{2}{3}(x - 3) \]
So, the point-slope form of the line is:
**y + 2 = (2/3)(x - 3)**
If we need to fill in the blanks according to the drag-and-drop format you've provided, here’s how it would look:
1. Fill in for \( y \):
- **y**
2. Fill in for \( y_1 \):
- **-2**
3. Fill in for \( m \):
- **2/3**
4. Fill in for \( x_1 \):
- **3**
Putting it all together in point-slope format using the listed variables and numbers:
\[ y - (-2) = \frac{2}{3}(x - 3) \]
If the slope was different and you need to adjust it based on specific provided values, feel free to swap out the slope \( \frac{2}{3} \) for another value you are working with, while keeping the point at \( (3, -2) \).
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
In this case, the point is \( (3, -2) \) and let's say the slope \( m \) is \( \frac{2}{3} \). Plugging in the values:
- \( x_1 = 3 \)
- \( y_1 = -2 \)
- \( m = \frac{2}{3} \)
We have:
\[ y - (-2) = \frac{2}{3}(x - 3) \]
This simplifies to:
\[ y + 2 = \frac{2}{3}(x - 3) \]
So, the point-slope form of the line is:
**y + 2 = (2/3)(x - 3)**
If we need to fill in the blanks according to the drag-and-drop format you've provided, here’s how it would look:
1. Fill in for \( y \):
- **y**
2. Fill in for \( y_1 \):
- **-2**
3. Fill in for \( m \):
- **2/3**
4. Fill in for \( x_1 \):
- **3**
Putting it all together in point-slope format using the listed variables and numbers:
\[ y - (-2) = \frac{2}{3}(x - 3) \]
If the slope was different and you need to adjust it based on specific provided values, feel free to swap out the slope \( \frac{2}{3} \) for another value you are working with, while keeping the point at \( (3, -2) \).