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: \( y + 8 = -3(x - 3) \)