To complete the point-slope equation of the line through the points [tex]\((-1, 6)\)[/tex] and [tex]\((1, 5)\)[/tex], we need to know the slope and then use the point-slope form of the line equation. Here is the detailed step-by-step solution:
1. Identify the coordinates:
- The first point is [tex]\((-1, 6)\)[/tex].
- The second point is [tex]\((1, 5)\)[/tex].
2. Calculate the slope (m):
- The slope formula is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- Substituting the given points [tex]\((-1, 6)\)[/tex] and [tex]\((1, 5)\)[/tex] into the formula:
[tex]\[
m = \frac{5 - 6}{1 - (-1)} = \frac{5 - 6}{1 + 1} = \frac{-1}{2} = -0.5
\][/tex]
3. Use the point-slope form of the line equation:
- The point-slope form for a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
- Using the point [tex]\((-1, 6)\)[/tex] and the slope [tex]\(m = -0.5\)[/tex], the equation becomes:
[tex]\[
y - 6 = -0.5 \cdot (x + 1)
\][/tex]
Therefore, the completed point-slope equation of the line through the points [tex]\((-1, 6)\)[/tex] and [tex]\((1, 5)\)[/tex] in exact numbers is:
[tex]\[
y - 6 = -0.5(x + 1)
\][/tex]
