Question

The table represents some points on the graph of a linear function.

-5
1
-19.5
1.5
Which equation represents the same relationship?
X
Oy 3.5x2
=
Oy=-3.5x + 2
Oy=-2x +3.5
Oy=2x-3.5
-1.5
-7.25
15.5
22.5

Answer 1

`\[ \text{{Option 2: }} y = -3.5x + 2 \]`

This is the correct equation that represents the given relationship based on the provided points.

To find the equation of the linear function represented by the given points, we can use the slope-intercept form of a linear equation:
`\(y = mx + b\)`, where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

First, let's find the slope
`(\(m\))` using two of the given points (-5, -19.5) and (1, 1.5):

`\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} \]`

`\[ m = \frac{{1.5 - (-19.5)}}{{1 - (-5)}} \]`

`\[ m = \frac{{21}}{{6}} \]`

`\[ m = 3.5 \]`

Now that we have the slope
`(\(m\))`, we can use one of the points to find the y-intercept
`(\(b\))`. Let's use the point (1, 1.5):

`\[ 1.5 = 3.5 * 1 + b \]`

`\[ b = 1.5 - 3.5 \]`

`\[ b = -2 \]`

So, the equation of the linear function is
`\(y = 3.5x - 2\)`.

Now, let's check which one of the provided options matches this equation:

`\[ \text{{Option 2: }} y = -3.5x + 2 \]`

This is the correct equation that represents the given relationship based on the provided points.