To find the equation of the line that passes through the given points, we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
First, let's find the slope \( m \) using two of the points, say (2, 1) and (1, 5):
The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using points (2, 1) and (1, 5): \[ m = \frac{5 - 1}{1 - 2} = \frac{4}{-1} = -4 \]
Now that we have the slope \( m = -4 \), we can use one of the points to find the y-intercept \( b \). Let's use the point (2, 1):
Substituting into the equation: \[ 1 = -4(2) + b \] \[ 1 = -8 + b \] \[ b = 1 + 8 = 9 \]
Now we have the slope \( m = -4 \) and the y-intercept \( b = 9 \). Therefore, the equation of the line is: \[ y = -4x + 9 \]
To fill in the blanks: \[ y = -4x + 9 \]
So, the correct responses for the boxes would be:
- \( -4 \) for the coefficient of \( x \)
- \( 9 \) for the constant term
Therefore, the complete equation is: \[ y = -4x + 9 \]