Questions: A line that includes the point (10,-3) has a slope of -8. 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.

Solution Steps

To find the equation of a line in point-slope form, we use the formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_1, y_1)\) is a point on the line. Given the point \((10, -3)\) and the slope \(-8\), we substitute these values into the formula to get the equation.

We are given the point \((10, -3)\) and the slope \(m = -8\).

Using the point-slope form of a linear equation, which is given by:

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

we substitute the values:

\[ y - (-3) = -8(x - 10) \]

This simplifies to:

\[ y + 3 = -8(x - 10) \]

Distributing \(-8\):

\[ y + 3 = -8x + 80 \]

Now, we isolate \(y\):

\[ y = -8x + 80 - 3 \]

Thus, we have:

\[ y = -8x + 77 \]

Final Answer