Final answer:
The complete equation of the line through the points (-9,7) and (-6,-3), using exact numbers, is y = (-10/3)x - 23.
Step-by-step explanation:
To complete the equation of the line that passes through the points (-9,7) and (-6,-3), we first need to find the slope (m) of the line. The slope is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
For our points (-9,7) and (-6,-3):
m = (-3 - 7) / (-6 - (-9)) = (-10) / (3) = -10/3
Now, we will use this slope and one of the points to find the equation of the line in the slope-intercept form (y = mx + b). Let's use the point (-9, 7):
7 = (-10/3)(-9) + b
After simplifying, we find that:
b = 7 - 30 = -23
Therefore, the complete equation of the line using exact numbers is:
y = (-10/3)x - 23.