Given the table with the coordinates, we can identify two points [tex]\((-10, 8)\)[/tex] and [tex]\((-5, 7)\)[/tex]. To determine the equation of the line in point-slope form, we can proceed with the following steps:
1. Calculate the slope:
The slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given:
[tex]\((x_1, y_1) = (-10, 8)\)[/tex]
[tex]\((x_2, y_2) = (-5, 7)\)[/tex]
Plugging in the values:
[tex]\[
m = \frac{7 - 8}{-5 - (-10)} = \frac{-1}{-5 + 10} = \frac{-1}{5} = -0.2
\][/tex]
2. Write the equation in point-slope form:
The point-slope form of the equation of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point [tex]\((-10, 8)\)[/tex] and the calculated slope [tex]\(m = -0.2\)[/tex], we substitute these values into the equation:
[tex]\[
y - 8 = -0.2(x - (-10))
\][/tex]
Simplify the term inside the parenthesis:
[tex]\[
y - 8 = -0.2(x + 10)
\][/tex]
Therefore, the equation of the line in point-slope form that uses the point [tex]\((-10, 8)\)[/tex] is:
[tex]\[
y - 8 = -0.2(x + 10)
\][/tex]
So, the correct option is:
[tex]\[
\boxed{y - 8 = -0.2(x + 10)}
\][/tex]
