Final answer:
To determine the line's equation using function notation for points (-6,-37) and (8,33), calculate the slope (m) using the formula. Applying point-slope form with slope 5 and point (-6,-37), the function notation is (f(x) = 5x - 7).
Step-by-step explanation:
To find the equation of the line using function notation for the points (-6,-37) and (8,33), we first need to calculate the slope (m) of the line. The slope formula is m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (33 - (-37)) / (8 - (-6)) = 70 / 14 = 5. With the slope found, we'll use the point-slope form to write the equation: y - y1 = m(x - x1). Picking the point (-6,-37), we substitute the values: y - (-37) = 5(x - (-6)). Simplifying, we get y + 37 = 5(x + 6), and further y + 37 = 5x + 30. Subtracting 37 from both sides gives us y = 5x - 7. Therefore, the function notation is f(x) = 5x - 7.