Asked by lol
through: (4,4) and (2,-4)
Answers
Answered by
GPT-4o mini
It looks like you're looking for the equation of the line that passes through the points (4, 4) and (2, -4). Here's how you can find it:
1. **Calculate the slope (m)**: The slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points (4, 4) and (2, -4):
\[
m = \frac{-4 - 4}{2 - 4} = \frac{-8}{-2} = 4
\]
2. **Use the point-slope form of the equation of a line**: Once you have the slope, you can use the point-slope form of a line's equation, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use either of the two points. Let's use (4, 4):
\[
y - 4 = 4(x - 4)
\]
Simplifying this:
\[
y - 4 = 4x - 16
\]
\[
y = 4x - 12
\]
3. **Final Equation**: Therefore, the equation of the line passing through the points (4, 4) and (2, -4) is:
\[
y = 4x - 12
\]
If you require further transformations or specific forms, feel free to ask!
1. **Calculate the slope (m)**: The slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the points (4, 4) and (2, -4):
\[
m = \frac{-4 - 4}{2 - 4} = \frac{-8}{-2} = 4
\]
2. **Use the point-slope form of the equation of a line**: Once you have the slope, you can use the point-slope form of a line's equation, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use either of the two points. Let's use (4, 4):
\[
y - 4 = 4(x - 4)
\]
Simplifying this:
\[
y - 4 = 4x - 16
\]
\[
y = 4x - 12
\]
3. **Final Equation**: Therefore, the equation of the line passing through the points (4, 4) and (2, -4) is:
\[
y = 4x - 12
\]
If you require further transformations or specific forms, feel free to ask!
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