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 1* or *blank 2*

Options for both blanks
Fill in 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) of the line that goes through the points (0, 8), (10, 4), and (20, 0), we can use the slope formula:

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

Let's use the points (10, 4) and (20, 0):

\[
M = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5}
\]
When expressed as a decimal, this would be -0.4.

Now, let's calculate the slope using the first and second points (0, 8) and (10, 4):

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

So the slope remains consistent.

Now, let's fill out the given options for the slope.

The correct option is:

- **C -10/4** (which simplifies to -2.5, and is not equal to -0.4).
- The other option is **G -4/10** (which is -0.4).

So, we fill the blanks with *G -4/10*.

The y-intercept (the value of Y when X = 0) from the points is given by the point (0, 8):

So the correct option is **C 8**.

Using the slope-intercept form of the equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can plug in our values:

\[
y = -0.4x + 8
\]

Thus, the equation of the line that represents the scenario is:

\[
y = -0.4x + 8
\]

So, to summarize:

- The slope in the blanks is **G -4/10**.
- The y-intercept in the blanks is **C 8**.
- The equation of the line is \( y = -0.4x + 8 \).