Question

Write an equation from slope-intercept form (

y
=
m
x
+
b
y=mx+b ) from the table below. Click Here for Help Video.

x
x
y
y
5
5
9
9
10
10
17
17
15
15
25
25





y

=
y =

x

+
x +

Answer 1

that's wrong fix it

Answer 2

To write the equation from slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \) from the given values.

From the provided table, we can take two points where \( (x, y) \) values are:

- Point 1: \( (5, 5) \)
- Point 2: \( (10, 10) \)

### Step 1: Calculate the Slope (m)

The formula for the slope \( m \) is:

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

Using the points \( (5, 5) \) and \( (10, 10) \):

\[
m = \frac{10 - 5}{10 - 5} = \frac{5}{5} = 1
\]

### Step 2: Find the Y-Intercept (b)

Now, we can use the slope \( m \) and one of the points to find the y-intercept \( b \). We can use the point \( (5, 5) \):

\[
y = mx + b
\]
\[
5 = 1(5) + b
\]
\[
5 = 5 + b
\]
\[
b = 5 - 5 = 0
\]

### Step 3: Write the Equation

Now that we have \( m = 1 \) and \( b = 0 \), we can write the equation:

\[
y = 1x + 0
\]
or simply:
\[
y = x
\]

So the final equation from slope-intercept form based on the given table is:

\[
y = x
\]

Answer 3

I apologize for the confusion. Let's carefully analyze the data provided in the table.

The table you provided appears to show pairs of \( (x, y) \) coordinates, and they are:

\[
\begin{align*}
(5, 5) \\
(9, 9) \\
(10, 10) \\
(17, 17) \\
(15, 15) \\
(25, 25) \\
\end{align*}
\]

This data actually suggests a linear relationship where \( y \) seems to equal \( x \) based on the pairs where \( y = x \).

However, let's double-check and derive the equation again properly.

### Calculate the Slope (m)

The change in \( y \) over the change in \( x \) can be checked with any two points. Let's use the points:

- \( (5, 5) \)
- \( (9, 9) \)

The slope formula \( m \) is:

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

Using the points \( (5, 5) \) and \( (9, 9) \):

\[
m = \frac{9 - 5}{9 - 5} = \frac{4}{4} = 1
\]

### Find the Y-Intercept (b)

We'll use one of the points again to find \( b \). Let's use \( (5, 5) \):

\[
y = mx + b
\]
Substituting \( m \) and the point \( (5, 5) \):

\[
5 = 1(5) + b
\]
\[
5 = 5 + b
\]
\[
b = 5 - 5 = 0
\]

### Final Equation

So the slope is \( 1 \) and the y-intercept is \( 0 \). Thus, the equation in slope-intercept form is:

\[
y = 1x + 0 \quad \text{or simply} \quad y = x
\]

This correctly represents the linear relationship evident in your provided data. All values of \( y \) correspond directly to their \( x \) values.

If there is additional context or you are looking for a different interpretation of the data, please let me know!