Question

Christa walks to school every day at the same pace.

After 5 minutes, she is 800 meters from school.

After 10 minutes, she is 300 meters away.

Here's a table for my questions

X (minutes that went by
0
5
10
Y meters away from school
1300
800
300
Question A What is the slope that goes through the points
Question b What's is the y-intercept

Options for question a

A 1/100

B 500

C 1/500

D 100

Options for Question b

A 800

B 1100

C 500

D 1300

E 300

What's is the equation of the line that represents the scenario

Answer 1

To find the slope and y-intercept from the given points, we can use the coordinates provided. The coordinates of the points based on the table are:

- Point 1: (5, 800)
- Point 2: (10, 300)

**Question A: Finding the Slope**

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting in our points:

\[
m = \frac{300 - 800}{10 - 5} = \frac{-500}{5} = -100
\]

This means for every minute that passes, Christa gets 100 meters closer to school.

From the options:
- A: \( \frac{1}{100} \)
- B: 500
- C: \( \frac{1}{500} \)
- D: 100

There are no matches, but the correct slope of \(-100\) translates to getting 100 meters closer, but it's negative indicating a decrease in distance.

**Question B: Finding the y-intercept**

The y-intercept (let's denote it as \( b \)) can be found using the slope-intercept form of the equation of a line, which is:

\[
y = mx + b
\]

Using one of the points. We can use Point 1 (5, 800):

\[
800 = -100(5) + b
\]
\[
800 = -500 + b
\]
\[
b = 800 + 500 = 1300
\]

From the options provided for the y-intercept:
- A 800
- B 1100
- C 500
- D 1300
- E 300

The correct answer is D: 1300.

### Conclusion

- **Slope**: The slope is -100 (although it's not one of the options).
- **Y-intercept**: The y-intercept is 1300 (D).

### The Equation of the Line

Substituting the values for the slope and y-intercept into the slope-intercept form:

\[
y = -100x + 1300
\]

This is the equation of the line that represents the scenario.