Question

x y
5 16.5
7 2.5
11 31.5

What are the slope and y intercept of the linear equation?


slope 2, y-intercept (0, 6.5)

slope -2, y-intercept (4,0)

slope -2.5, y-intercept (4,0)

slope 2.5, y-intercept (0,4)

Answer 1

sorry,

x y
5 16.5
7 21.5
11 31.5

Answer 2

To determine the slope and y-intercept of the linear equation that fits the given points, we can first calculate the slope (\(m\)) using the formula:

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

We can use any two points from the dataset. Let's use the points (5, 16.5) and (7, 2.5):

1. \( (x_1, y_1) = (5, 16.5) \)
2. \( (x_2, y_2) = (7, 2.5) \)

Calculating the slope:

\[
m = \frac{2.5 - 16.5}{7 - 5} = \frac{-14}{2} = -7
\]

Next, we can use one of the points and the slope to find the y-intercept (\(b\)) using the equation of a line \(y = mx + b\).

Using the point (5, 16.5):

\[
16.5 = -7(5) + b
\]
\[
16.5 = -35 + b
\]
\[
b = 16.5 + 35 = 51.5
\]

Hence, the linear equation is:

\[
y = -7x + 51.5
\]

Now, let's double-check using another pair of points, such as (7, 2.5) and (11, 31.5):

Using (7, 2.5) and (11, 31.5):

1. \( (x_1, y_1) = (7, 2.5) \)
2. \( (x_2, y_2) = (11, 31.5) \)

Calculating the slope:

\[
m = \frac{31.5 - 2.5}{11 - 7} = \frac{29}{4} = 7.25
\]

But since the slope we found previously is already not matching, it seems we have made a calculation error.

To summarize, I will check if the original calculations for multiple points yield a consistent line. If these calculations were performed correctly:

- Various combinations lead to different slopes inconsistent with both given options of y-intercepts.

Thus, the pairs of points do lead me towards checking the outputs correctly.

So, we can summarize:

- The slope and intercept from earlier calculations might not point towards strong fit unless further checked herein the options provided.

None of the given multiple-choice answers match this due to errors in slopes.

If you need further help, please ask!

Answer 3

No problem! Let's find the slope and y-intercept with the new set of points you've provided:

1. \( (5, 16.5) \)
2. \( (7, 21.5) \)
3. \( (11, 31.5) \)

### Step 1: Calculate the slope

We can calculate the slope using two points, say (5, 16.5) and (7, 21.5):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{21.5 - 16.5}{7 - 5} = \frac{5}{2} = 2.5
\]

### Step 2: Calculate the y-intercept

Now, we can use the slope and one of the points to find the y-intercept (\(b\)). We'll use the point (5, 16.5):

Using the formula \(y = mx + b\):

\[
16.5 = 2.5(5) + b
\]
\[
16.5 = 12.5 + b
\]
\[
b = 16.5 - 12.5 = 4
\]

### Conclusion

The slope is \(2.5\) and the y-intercept is \(4\).

Thus, the equation of the line is:

\[
y = 2.5x + 4
\]

Given your options, the correct answer is:

**Slope 2.5, y-intercept (0, 4)**.