Consider the equation of the line that goes through the points \( (3,7) \) and \( (-1,-5) \). Fill in the blanks below. Note: Your answers should be integers. The slope of this line is The \( y \)-intercept of this line is

To find the slope of the line that goes through the points \( (3,7) \) and \( (-1,-5) \), we use the formula for the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we can assign: - \( (x_1, y_1) = (3, 7) \) - \( (x_2, y_2) = (-1, -5) \) Now, substituting the values into the slope formula: \[ m = \frac{-5 - 7}{-1 - 3} = \frac{-12}{-4} = 3 \] So, the slope of the line is \( 3 \). Next, we need to find the \( y \)-intercept of the line. We can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Using the point \( (3, 7) \) and the slope \( m = 3 \): \[ y - 7 = 3(x - 3) \] Expanding this equation: \[ y - 7 = 3x - 9 \] Adding \( 7 \) to both sides: \[ y = 3x - 2 \] From this equation, we can see that the \( y \)-intercept (the value of \( y \) when \( x = 0 \)) is \( -2 \). Thus, we fill in the blanks: The slope of this line is \( 3 \). The \( y \)-intercept of this line is \( -2 \).