Question

A line passes through the points (-2, 7) and (3, -8).
Part II: Given the slope (calculated in Part I) and the two points, write TWO EQUATIONS in point-slope form of the line.

Equation 1: _____________

Equation 2: _____________

Answer 1

To write the equations in point-slope form, we first need to calculate the slope of the line that passes through the points (-2, 7) and (3, -8).

**Step 1: Calculate the slope (m)**

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-2, 7)\) and \((3, -8)\):

\[
x_1 = -2, \quad y_1 = 7, \quad x_2 = 3, \quad y_2 = -8
\]

Plugging in the values:

\[
m = \frac{-8 - 7}{3 - (-2)} = \frac{-15}{3 + 2} = \frac{-15}{5} = -3
\]

The slope of the line (m) is -3.

**Step 2: Write the equations in point-slope form**

The point-slope form of a line is given by:

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

We can use either point to create the equations.

**Using the point (-2, 7):**

\[
y - 7 = -3(x - (-2))
\]

This simplifies to:

\[
y - 7 = -3(x + 2)
\]

**Equation 1:**

\[
y - 7 = -3(x + 2)
\]

**Using the point (3, -8):**

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

This simplifies to:

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

**Equation 2:**

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

So the two equations in point-slope form are:

**Equation 1: \( y - 7 = -3(x + 2) \)**

**Equation 2: \( y + 8 = -3(x - 3) \)**