A line that includes the point (5,

Question

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6) has a slope of
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5. What is its equation in point-slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

Answer 1

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, we have the point \((5, -6)\) and the slope \(m = -5\).

Substituting the values into the point-slope formula:

\[ y - (-6) = -5(x - 5) \]

This simplifies to:

\[ y + 6 = -5(x - 5) \]

This is the equation of the line in point-slope form. It can also be left in this format or expanded further if necessary, but since you requested the point-slope form, the final answer is:

\[ y + 6 = -5(x - 5) \]