What is the point-slope equation of the line with slope -10 that goes through the point (1,4)?

The point-slope form of the equation of a line can be expressed as:

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

where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.

Given that the slope \( m = -10 \) and the point \( (x_1, y_1) = (1, 4) \), we can substitute these values into the point-slope form:

\[ y - 4 = -10(x - 1) \]

This is the point-slope equation of the line. If you want to simplify it or convert it to slope-intercept form, you can distribute and rearrange:

\[ y - 4 = -10x + 10 \]

Adding 4 to both sides gives:

\[ y = -10x + 14 \]

But the point-slope form \( y - 4 = -10(x - 1) \) is sufficient as the answer.

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