Final answer:
To find a line perpendicular to y=-1/2x+3 and goes through the point (3,-6), we need to determine the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line. The perpendicular line will have a slope of 2. Using the point-slope form of a line equation, we can determine the equation of the perpendicular line to be y = 2x - 12.
Step-by-step explanation:
To find a line perpendicular to y = -1/2x + 3 and goes through the point (3, -6), we need to determine the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line. The given line has a slope of -1/2. The negative reciprocal of -1/2 is 2. So, the perpendicular line will have a slope of 2. We can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values (3, -6) and 2 into the equation, we get: y - (-6) = 2(x - 3). Simplifying, we have y + 6 = 2x - 6. To find the equation in slope-intercept form, we isolate y by subtracting 6 from both sides: y = 2x - 12. Therefore, the line perpendicular to y = -1/2x + 3 and goes through the point (3, -6) is y = 2x - 12.