Question

The table represents a linear equation.

A two column table with 5 rows. The first column, x, has the entries, negative 10, negative 5, 10, 15. The second column, y, has the entries, 8, 7. 4, 3.
Which equation shows how (–10, 8) can be used to write the equation of this line in point-slope form?

y – 8 = –0.15(x – 10)
y + 8 = –0.15(x – 10)
y – 8 = –0.2(x + 10)
y + 8 = –0.2(x – 10)

Answer 1

To find the equation in point-slope form that can be used with the point \((-10, 8)\), we first need to determine the slope of the line using the provided points.

The given points are:
- (-10, 8)
- (-5, 7)
- (10, 4)
- (15, 3)

To find the slope (m) of the line, we can take any two points. Let's use \((-10, 8)\) and \((-5, 7)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 8}{-5 - (-10)} = \frac{-1}{5} = -0.2
\]

Now we have the slope \(m = -0.2\).

The point-slope form of a linear equation is given by:

\[
y - y_1 = m(x - x_1)
\]

Using the point \((-10, 8)\) \((x_1 = -10, y_1 = 8)\) and the slope \(m = -0.2\), we can write:

\[
y - 8 = -0.2(x - (-10)) \implies y - 8 = -0.2(x + 10)
\]

Thus, the correct option from the ones provided is:

**y - 8 = -0.2(x + 10)**.