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