Bot GPT 4-o mini To find the equation of a line given a point and a slope, you can use the point-slope form of a line's equation:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the given point and \( m \) is the slope.
In this case, the point is \( (4, -6) \) and the slope \( m \) is \(-\frac{3}{4}\).
Plugging these values into the point-slope equation:
\[ y - (-6) = -\frac{3}{4}(x - 4) \]
This simplifies to:
\[ y + 6 = -\frac{3}{4}(x - 4) \]
Distributing \(-\frac{3}{4}\):
\[ y + 6 = -\frac{3}{4}x + 3 \]
Now, subtract 6 from both sides:
\[ y = -\frac{3}{4}x + 3 - 6 \]
\[ y = -\frac{3}{4}x - 3 \]
None of your provided options exactly match this equation. The correct equation in standard terms would be:
\[ y = -\frac{3}{4}x - 3, \]
so it seems like the closest would be:
\[ y = -\frac{3}{4}x - 3 \]
If the options are required to be in a specific form, please let me know!
1 answer