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Since the problem statement only gives us one point, we need to use point-slope form to find the equation of this line, instead of two-point form. Since we have the point (7,-2), we need to figure out what the slope of the line needs to be. If our line needs to be perpendicular to the line given in the problem statement, first we need to figure out the slope of THAT line. The equation of that line is x+3y=15, or y = -(1/3)x + 5. The slope of the line is -1/3. A perpendicular line must have a slope that is the negative reciprocal of -1/3, thus the slope must be 3.
Now we know that our line must go through the point (7,-2) and should have a slope 3. We can use point-slope form: y-y1 = m(x-x1), where y1 = -2, x1 = 7, and m = 3. We have y+2 = 4(x-7), or y + 2 = 4x - 28, or y = 4x - 30, which is the solution.
Please let me know if you need any clarification. I'm always happy to answer your questions.