Question

Christa's friend Edrei takes the bus to school.

She starts at a distance of 8 miles from the school.
After 10 minutes on the bus, she is 4 miles from the school.
After 20 minutes, she is O miles from the school.

X (minutes that went by)
0
10
20
Y (miles away from school)
8
4
0

What is the slope that goes throught the points


M = *blank* or *blank

Options for both blanks

A 4

B 10

C -10/4

D -10

E 10/4

F -4

G - 4/10

What is the y-intercept of the line that goes through points

A 4
B 10
C 8
D 0
E 20


What is the equation of the line that represents the scenario? Use the decimal value for slope.

Answer 1

To find the slope \( M \) that goes through the points, we can use the formula for slope:

\[
M = \frac{Y_2 - Y_1}{X_2 - X_1}
\]

Let's take the first two points \((0, 8)\) and \((10, 4)\):

\[
M = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5} = -0.4
\]

Now, we'll also check the slope between the second point \((10, 4)\) and the third point \((20, 0)\):

\[
M = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5} = -0.4
\]

Since both calculations give the same result, the slope \( M \) is consistent.

### Slope Choices:
The options given do not include -0.4. Let’s express -0.4 in terms of the options provided:

- -0.4 can be represented as \(-\frac{4}{10}\).
- Checking against the list:
- C: -10/4 (Not equal to -0.4)
- D: -10 (Not equal to -0.4)
- F: -4 (Not equal to -0.4)
- G: -4/10 (Not equal to -0.4, equals -0.4 after simplification)
- Thus, the correct answer for the slope that fits the line is **G: -4/10**.

### Y-Intercept:
The y-intercept occurs when \( X = 0 \). From the given points, at \( X = 0 \), \( Y = 8 \).

### Y-Intercept Choices:
According to the choices given:
- C: 8 (Correct)

### Equation of the Line:
The equation of the line can be expressed in slope-intercept form \( Y = MX + B \).

Where:
- \( M = -0.4 \) or \( -\frac{2}{5} \)
- \( B = 8 \)

Thus, the equation of the line is:

\[
Y = -0.4X + 8
\]

Summarizing:
- **Slope \( M \): -4/10**
- **Y-intercept \( B \): 8**
- **Equation of the line: \( Y = -0.4X + 8 \)**