Final answer:
The equation of the line with a slope of -8 that passes through the point (2,9) is y = -8x + 16.
Step-by-step explanation:
The student is asking for the equation of a line with a slope (m) of -8 that passes through the point (2,9). In mathematics, the equation of a straight line is generally represented by y = mx + b, where m is the slope of the line, and b is the y-intercept, the point where the line crosses the y-axis. To find the equation of our specific line, we need to use the given slope (-8) and the given point to solve for b.
Step 1: Start with the point-slope form of the equation: y - y1 = m(x - x1).
Step 2: Substitute the given point (2,9) and the slope (m = -8) into the equation: 9 - y1 = -8(2 - x1).
Step 3: Solve for y1 by expanding the right side: 9 = -8x + 16 + y1.
Step 4: Finally, isolate y to get the y-intercept (b): 9 = -8x + 16, so b = 16. Therefore, the equation of the line is y = -8x + 16.