The table represents a linear equation.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-10 & 8 \\
\hline
-5 & 7 \\
\hline
10 & 4 \\
\hline
15 & 3 \\
\hline
\end{tabular}

Which equation shows how [tex]$(-10, 8)$[/tex] can be used to write the equation of this line in point-slope form?

A. [tex]$y - 8 = -0.15(x - 10)$[/tex]

B. [tex]$y + 8 = -0.15(x - 10)$[/tex]

C. [tex]$y - 8 = -0.2(x + 10)$[/tex]

D. [tex]$y + 8 = -0.2(x - 10)$[/tex]



Answer :

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]