Question

Write the slope-intercept equation of the function f whose graph satisifies the given conditions The graph of f passes through(-12,8) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of 15 The equation of the function is ork lan (Use integers or fractions for any numbers in the equation.) ook

Answer 1

Standard equation of a line having x-intercept,a = 5 and y-intercept,b = -15 is, x/5 + y/(-15) = 1

=> x/5 - y/15 = 1=> 3x-y/15 = 1

=> 3x-y = 15 => y = 3x-15

Which is in slope intercept form of the line with slope of 3. Now if m and m' be the slopes of two mutually perpendicular lines, then, m×m' = -1

So, the slope of the required line,m = - 1/3

Now equation of a line passing through a point (x',y') and having slope m is, (y-y') = m(x-x')

Thus, equation of the required line,

y-8 = (- 1/3){x-(-12)}

=> 3(y-8) = -(x+12)

=> 3y-24 = -x-12 => 3y = -x+12

=> y = (- 1/3)x + 4

Hence, required equation of the line in slope intercept form is, y = (- 1/3)x + 4

with slope = (- 1/3) and y-intercept = 4.