A table of values is shown.

 

 

x

 

−8
−4
2
5
 

y

 

8
112
 74
 	−18
 

Which equation models the relationship in the table?

	
y+8=−85(x−8)

	
y+8=−58(x−8)

	
y−8=−58(x+8)

	
y−8=−85(x+8)

We are given a table of values and need to determine which equation models the relationship between \(x\) and \(y\). The equation choices are in point-slope form, which is expressed as:

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

where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.

We need to:
1. Find the slope \(m\) using two points from the table.
2. Match the slope and one of the given points to the correct equation.

### Step 1: Find the slope \(m\)
The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's take the points \((-8, 8)\) and \((2, 74)\):

\[
m = \frac{74 - 8}{2 - (-8)} = \frac{66}{10} = 6.6
\]

So, the slope \(m = 6.6\).

### Step 2: Match the equation form
Now, let's compare the given equations to see which one fits:

- First, check the form of the point-slope equation. We can see that all the given choices are structured as transformations of the point-slope form.
- The correct slope should be approximately \(-58\) or \(-85\), none of which directly matches, suggesting we need to recheck the match point.

A table of values is shown. 

x: -8, -4, 2, 5 

y: 8, 112, 74, -18 

Which equation models the relationship in the table?

1. y+8=−85(x−8) 
2. y+8=−58(x−8) 
3. y−8=−58(x+8) 
4. y−8=−85(x+8)

This problem helps you determine which linear equation models the relationship between x and y in a table of values. Learn how to use the slope formula and point-slope form to find the correct equation. Ideal for students in Grades 8-10.

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