The graph of cubical function y = a (x) ^3 + b (x) ^2 +c (x) + d which goes through the points (0, 1), (−1, −2), (1, 2), (2, 9). what is the value of a, b and c?​

If a line is perpendicular to another line, then the product of the slopes of the two lines is -1.

Therefore, if m1 and m2 are the slopes of the two lines then m1.m2 = -1

Now the slope of line y = 4x+3 can be obtained by comparing the equation of the line with y = mx+c where m = slope of the line and c = y-intercept.

Therefore we can say that the slope of this line (i.e. m1) = 4.

Therefore, the slope of the line perpendicular to this line is (i.e. m2) = -1/4

Now the general equation of the 2nd line can be written as

y = (-1/4)x+c   1)

Since, point (-12,4) lies on this line we can substitute the value of y = -12 and x = 4 in the above equation to find the value of c.

Once we find the value of c, we can complete the equation for the line which is perpendicular to line y = 4x+3