Will make the system of equations with a linear equation so that the graphs of the equations intersect at their x- and y-intercepts. y= x^3-3x^2+x-3

First, we have to find x- and y-intercepts of given equation.

1. y-intercept is a point (0, y) so substitute x = 0 and calculate:



y-intercept = (0, -3)

2. x-intercept is a point (or points) (x, 0), so when we substitute y = 0 there will be:



x-intercept = (3, 0)

Now, when we have x- and y-intercepts, we can write an equation of a line (graph of the linear function) that passes through this two points:



Our linear equation is: y = x - 3