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#