Given the graph of a linear function, find the linear equation of the graph in point-slope form. What is the missing value needed to finish the point-slope form of the equation?

Question

The points are (-2,8 ) , (-1, 5) ,(0,2) , (1, -1) ,(2,-4)

The point-slope form of the equation is y-___ = -3 (x-1)

Answer 1

To find the missing value in the point-slope form of the linear equation, we first need to identify the slope of the line defined by the points given.

The points provided are: (-2, 8), (-1, 5), (0, 2), (1, -1), (2, -4).

Let's calculate the slope (m) using two points from the data. We can use points (-1, 5) and (0, 2):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 5}{0 - (-1)} = \frac{-3}{1} = -3. \]

Now, we can use the slope of -3 and one of the points to write the point-slope form of the equation. The point-slope form is given by:

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

Using the point (1, -1) (which is one of the points given), we substitute \(y_1 = -1\), \(m = -3\), and \(x_1 = 1\):

\[ y - (-1) = -3(x - 1). \]

This simplifies to:

\[ y + 1 = -3(x - 1). \]

Now, rearranging to match the point-slope form:

Thus, in the point-slope form \(y - __ = -3(x - 1)\), the missing value is:

\(-1\).

So, the final answer is:

-1.