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
−
7
−7
−
5
−5
0
0
4
4
7
7
13
13
14
14
22
22





y

=
y =

x

+
x +

Answer 1

y is wrong

Answer 2

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

The given points from the table are:
- \( (-7, -7) \)
- \( (-5, -5) \)
- \( (0, 4) \)
- \( (7, 7) \)
- \( (13, 13) \)
- \( (14, 14) \)
- \( (22, 22) \)

First, we can calculate the slope \( m \) using two points. Let's use the points \( (-7, -7) \) and \( (0, 4) \):

1. Calculate the slope \( m \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-7)}{0 - (-7)} = \frac{4 + 7}{0 + 7} = \frac{11}{7}
\]

2. Using the point-slope form of the line equation, we can use one of the points, say \( (0, 4) \), to find \( b \):

\[
y = mx + b
\]
Substituting \( m = \frac{11}{7} \) and using the point \( (0, 4) \):

\[
4 = \frac{11}{7}(0) + b \\
b = 4
\]

Thus, the equation in slope-intercept form is:

\[
y = \frac{11}{7}x + 4
\]

If you want a whole number slope, we can also use other points or refer to the tables more broadly to identify a consistent relationship. In this case, it appears the line might be more comprehensive relative to \( y = x \) + constant shifts based on the points' distribution.

However, based strictly on calculations from the two points specified earlier, our derived equation stands as correct based on the linear relationship witnessed through the provided values. So the final answer is:

\[
y = \frac{11}{7}x + 4
\]

Answer 3

I apologize for the confusion. Let's find the correct slope-intercept form \(y = mx + b\) based on the provided values.

Given the points in the table:
- \( (-7, -7) \)
- \( (-5, -5) \)
- \( (0, 4) \)
- \( (7, 7) \)
- \( (13, 13) \)
- \( (14, 14) \)
- \( (22, 22) \)

It appears that there may have been an oversight in interpreting the relationship among the points.

Let's observe both x and y-values:

- For \( x = -7 \), \( y = -7 \)
- For \( x = -5 \), \( y = -5 \)
- For \( x = 0 \), \( y = 4 \)
- For \( x = 7 \), \( y = 7 \)
- For \( x = 13 \), \( y = 13 \)
- For \( x = 14 \), \( y = 14 \)
- For \( x = 22 \), \( y = 22 \)

It's clear that there's a pattern, but first we also need to find two specific points where we can compute the slope.

### Points
Let’s check the first two points to establish a clear slope as:
1. **Point 1:** \( (-7, -7) \)
2. **Point 2:** \( (7, 7) \)

### Slope Calculation

Using the points \( (-7, -7) \) and \( (7, 7) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - (-7)}{7 - (-7)} = \frac{7 + 7}{7 + 7} = \frac{14}{14} = 1
\]

### Finding the y-intercept \(b\)

Substituting the slope \(m = 1\) into the slope-intercept form using point \( (0, 4) \):

\[
y = mx + b \\
4 = 1(0) + b \\
b = 4
\]

### Final Equation

Putting it all together, we have:

\[
y = 1x + 4 \quad \text{or simply} \quad y = x + 4
\]

### Final Result

Thus the correct equation in slope-intercept form is:

\[
y = x + 4
\]

Thank you for your patience. If you have any more questions or need further assistance, feel free to ask!