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 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 blank 1
A 4

B 10

C -10/4

D -10

E 10/4

F -4

G - 4/10

Options for blank 2
A -10
B -4
C 4
D -2.5
E 0.4
F 10
G 2.5
H -0.4
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 (which are (0, 8), (10, 4), and (20, 0)), we can use the formula for slope:

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

Let's calculate the slope between the points (0, 8) and (10, 4):

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

So the slope (M) is -0.4.

Now let's find the slope between the points (10, 4) and (20, 0):

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

The slope remains consistent in both cases, confirming that the slope going through the points is -0.4.

For the options provided:

• For blank 1, the corresponding value from the options for -4/10 or -0.4 is H (-0.4).
• Therefore, the slope (M) options: C -10/4 = -0.4 or G -4/10 = -0.4.

Next, we find the y-intercept of the line. The y-intercept occurs when X = 0. Using the first point (0, 8), we see that when \(X = 0\), \(Y = 8\).

So the y-intercept is C 8.

Finally, to find the equation of the line, we can use the slope-intercept form of the equation, which is:

\[ Y = MX + b \]

Where \(M\) is the slope and \(b\) is the y-intercept. Plugging in the values we found:

\[ Y = -0.4X + 8 \]

Thus, the final answers are:

• Slope (M): H -0.4
• Y-intercept: C 8
• Equation of the line: \(Y = -0.4X + 8\)