Question

a side of a graph is shown with a negative slop with two dots are shown
dot 1: (1, 5)
dot 2: (2, 1)

Fill in the blank:
Y = (BLANK)x + (BLANK)

A. -9
B. -5
C. -4
D. -2
E. -1
F. 0
G. 1
H. 2
I. 4
J. 5
K. 9

Answer 1

To find the equation of the line in the form \( Y = mx + b \), we need to calculate the slope \( m \) first using the two points provided: (1, 5) and (2, 1).

The formula for the slope \( m \) is given by:

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

Substituting the points:

- \( (x_1, y_1) = (1, 5) \)
- \( (x_2, y_2) = (2, 1) \)

We have:

\[
m = \frac{1 - 5}{2 - 1} = \frac{-4}{1} = -4
\]

Next, we now have the slope \( m = -4 \). To find the y-intercept \( b \), we can use one of the points. Using the point (1, 5):

\[
Y = mx + b
\]
\[
5 = -4(1) + b
\]
\[
5 = -4 + b
\]
\[
b = 5 + 4 = 9
\]

Now we can write the equation of the line:

\[
Y = -4x + 9
\]

Filling in the blanks \( Y = (BLANK)x + (BLANK) \):

- The first blank (slope \( m \)) is \(-4\) (C).
- The second blank (y-intercept \( b \)) is \(9\) (K).

So the complete equation is:

\[
Y = -4x + 9
\]

The answer is:
- **First Blank:** C. -4
- **Second Blank:** K. 9