Question

Write a function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x).

Answer 1

The function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Given the equation of a line in standard form as y = 9x - 8

Get the slope of the line

mx = 9x

m = 9

Since the line passes through the origin (0, 0), substitute the slope and the point in the  point-slope form of the equation as shown below:

$y-y_0=m(x-x_0)$

$y-0=9(x-0)\\y =9x$

Hence the function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

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