Write the slopeintercept equation of the function f whose gr

Write the slope-intercept equation of the function f whose graph satisifies the given conditions. The graph of f passes through (-4, 5) and is perpendicular to the line that has an x-intercept of 2 and a y-intercept of -4. 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 2 and the y-intercept of -4 be y = mx+c. Since the y-intercept is where x = 0, we have c = -4. Then the equation of this line changes to y = mx-4. Also, the x-intercept is where y = 0,so that 0= m(2)-4 or, 2m = 4. Hence m = 4/2 = 2. Then the equation of this line is y = 2x-4. The slope of a line perpendicular to thius line is -1/2. Let the equation of the required line be y = -x/2+ a. Now, since this line passes through the point (-4,5), on substituting x = -4 and y = 5 in its equation, we get 5 = (-1/2)(-4)+a or, 5 = 2+a or, a +2=5. Hence a = 5-2 = 3. Thus, the equation of the required line is y = -x/2 +3.