To find the equation of the line through the points (11, -3) and (7, 9), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where (x1, y1) is one of the given points and m is the slope of the line.
First, let's calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (9 - (-3)) / (7 - 11)
m = 12 / (-4)
m = -3
Now, let's choose one of the points, such as (11, -3), and substitute the values into the point-slope form:
y - (-3) = -3(x - 11)
y + 3 = -3x + 33
y = -3x + 30
Therefore, the equation of the line through the points (11, -3) and (7, 9) is y = -3x + 30.
The correct option is C. y = -3x + 30.