Write the slopeintercept equation of the function f whose gr

Write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-8, 6) and is perpendicular to the line that has an x-intercept of 4 and a y-intercept of - 8. The equation of the perpendicular line is f(x) = (Use integers or fractions for any numbers in the expression.)

Solution

Let the equation of the line having x-intercept of 4 and the y-intercept of -8 be y = mx+c. Since the y-intercept is where x = 0, we have c = -8. Then the equation of this line changes to y = mx-8. Also, the x-intercept is where y = 0, so that 0= m(4)-8 or, 4m = 8. Hence m = 8/4 = 2. Then the equation of this line is y = 2x-8. The slope of a line perpendicular to this line is -1/2. Let the equation of the required line be y = -x/2+ b. Now, since this line passes through the point (-8,6), on substituting x = -8 and y = 6 in its equation, we get 6 = (-1/2)(-8)+b or, 6 = 4+b Hence b = 6-4 = 2. Thus, the equation of the required line is y = -x/2 +2