Christa's friend Edrei takes the bus to school.

Question

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 0 miles from the school

Table bellow

X (minutes that went by)
0
10
20

Y (miles away from school

8
4
0

What is the slope of the line that goes throught the points

M = *blank 1* *blank 2*
Fill both blanks with different Answers
Options for blank 1

A 4
B 10/4
C -4
D -10/4
E 4/10
F ‐4/10
G 10
H -10

Options for blank 2

A 0.4

B 10

C -2.5

D 2.5

E -4

F 4

G -10

H -0.4

The y-intercept is

A 8
B 20
C 10
D 0
E 4

What is the equation of the line that represents the scenario use the decimal value for the slope

Y = *blank 1* × + *blank 2*

Fill in the blanks

Answer 1

To find the slope (M) of the line that connects the points, we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Using the points \( (0, 8) \) and \( (20, 0) \):

• \( x_1 = 0, y_1 = 8 \)
• \( x_2 = 20, y_2 = 0 \)

Calculating the slope:

\[ M = \frac{0 - 8}{20 - 0} = \frac{-8}{20} = -\frac{2}{5} = -0.4 \]

Now let's match this slope with the options provided.

For blank 1:

The options are:

• C -4
• F -4/10

The correct answer, adjusted to the same denomination, is F -4/10 (which simplifies to -0.4, confirming that it is indeed the correct slope).

For blank 2:

Taking the y-intercept (where \(x = 0\)), we look at the data: when \(x = 0\), \(y = 8\). Thus, the correct answer is A 8 (the y-intercept).

So the correct answers filled in are:

• Blank 1: F -4/10
• Blank 2: A 8

The y-intercept (as found) is A 8.

Finally, to find the equation of the line, we can use the slope-intercept form \(Y = mX + b\).

Substituting the slope \(-0.4\) and the y-intercept \(8\): \[ Y = -0.4X + 8 \]

So, filling in the blanks for the equation of the line:

• Blank 1: -0.4
• Blank 2: 8

Thus, the equation is: \[ Y = -0.4X + 8 \]