To complete the point-slope equation of the line through the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex], let's go through the steps in detail:
1. Identify the points: We are given the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex].
2. Determine the slope:
- The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- Substituting our points:
[tex]\[
m = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7
\][/tex]
3. Write the point-slope form equation:
- The point-slope form of a line equation is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
- Here, [tex]\( (x_1, y_1) = (-5, 7) \)[/tex] and [tex]\( m = -7 \)[/tex].
4. Substitute the known values into the equation:
[tex]\[
y - 7 = -7(x - (-5))
\][/tex]
5. Simplify the equation:
- Since [tex]\( x - (-5) \)[/tex] simplifies to [tex]\( x + 5 \)[/tex]:
[tex]\[
y - 7 = -7(x + 5)
\][/tex]
Therefore, the complete point-slope equation of the line is:
[tex]\[
y - 7 = -7(x + 5)
\][/tex]
