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 = *A blank 1* *A blank 2*

Use the options provided

Options for A blank 1

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

Options for A 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 = *B blank 1* × + *B blank 2*

Fill in the blanks

Answer 1

To calculate the slope (M) of the line that goes through the points \((0, 8)\) and \((20, 0)\), we can use the formula for the slope of a line:

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

Using the points:

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

Substituting the values into the slope formula gives:

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

Now let's simplify \(-\frac{2}{5}\) as a decimal:

\(-\frac{2}{5} = -0.4\)

Fill in the Blanks for Slope:

A blank 1: C -4 (Note: The actual decimal value is -0.4, but it’s not listed in the options) A blank 2: H -0.4 (since \(M = -\frac{2}{5} = -0.4\))

Y-Intercept:

The y-intercept occurs when \(x = 0\). From the coordinate \((0, 8)\), the y-intercept is \(8\).

So for y-intercept: A: A 8

Equation of the line:

The equation of a line in slope-intercept form is given by:

\[ Y = Mx + b \]

Here, \(M = -0.4\) (slope) and \(b = 8\) (y-intercept).

The equation becomes: \[ Y = -0.4x + 8 \]

Fill in the Blanks for Equation:

B blank 1: -0.4
B blank 2: 8

Final answers are:

• A blank 1: C -4
• A blank 2: H -0.4
• Y-intercept: A 8
• Equation: \(Y = -0.4x + 8\)