Please help me determine the equation of the line in slope intercept form and show all work. A line that is perpendicular to the liney = (1/2)x + 10 that passes through thepoint (50,60).

Answer:y=-2x+160Step by Step:The equation of a line can be determined using the point slope formula:y-y1=m (x-x1)To make a substitution, we must ensure we have the correct information. The question gives:y1=60x1=50y=1/2x+10 This is the formula of a line that is perpendicular to the one we are trying to find.It tells us that the gradient of the perpendicular line is 1/2. The gradient of the line we are trying to find can be found using m1×m2=-1 because we know that when lines are perpendicular, the product of their gradients must equal 1So if we replace m1 with 1/21/2×m2=-1m2=-2We now have all the relevant information to make a substitution:y-60=-2 (x-50)expand bracketsy-60=-2x+100rearrange to get in the form y=mx+by=-2x+160