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

Question

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?

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Answer 1 · 2017-11-19T02:25:18

$y=7/3 x - 7$

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

$y=mx+b$

$y=7/3 x - 7$