Find the equation of the line through the y-intercept?

Find the equation of the line through the y-intercept of y=x^4-8x^5-7+6x^2 and the x intercept of y=3x-9?

1 Answer
Nov 19, 2017

y=7/3 x - 7

Explanation:

The y-intercept of y=x^4-8x^5-7+6x^2 occurs where x=0.

y=(0)^4-8(0)^5-7+6(0)^2=-7

The x-intercept of y=3x-9 occurs where y=0.

0=3x-9

9=3x

9/3=(3x)/3

x=3

So the question is what line goes through the points (0,-7) and (3, 0). The equation for the slope of a line is given as

m = (y_2-y_1)/(x_2-x_1)

m=(0-(-7))/(3-0)=7/3

The y-intercept b can be determined by plugging in the slope and one of the two points (it doesn't matter which one).

y=mx+b

-7=7/3(0) + b

b=-7

With m=7/3 and b=-7, the equation of a line becomes

y=mx+b

y=7/3 x - 7