Question
A line that includes the point (5,
–
6) has a slope of
–
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.
–
6) has a slope of
–
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.
Answers
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, 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:
\[
y + 6 = -5(x - 5)
\]
\[
y - y_1 = m(x - x_1)
\]
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:
\[
y + 6 = -5(x - 5)
\]