Question

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?

Answer 1

`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`