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aksik [14]
3 years ago
13

Write an equation of a line (-4,-1) and is perpendicular to the line y=4/3x+6 y =

Mathematics
1 answer:
NikAS [45]3 years ago
5 0

Answer:

y= -3/4x-2

Step-by-step explanation:

- perpendicular: opposite signs and reciprocal

m= -3/4

point-slope form: y-y1=m(x-x1)

y-(-1)= -3/4(x-(-4))

y+1= -3/4(x+4)

y+1= -3/4x -3

y= -3/4x-2

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A parabola is a quadratic function, and a quadratic can be expressed in vertex form, which is:

y=a(x-h)^2+k, where (h,k) is the vertex (absolute maximum or minimum point of the quadratic)

In this case we are given that (h,k) is (-5,80) so we have so far:

y=a(x--5)^2+80

y=a(x+5)^2+80, we are also told that it passes through the point (0,-45) so:

-45=a(0+5)^2+80

-45=25a+80  subtract 80 from both sides

-125=25a  divide both sides by 25

-5=a, so now we know the complete vertex form is:

y=-5(x+5)^2+80

The x-intercepts occur when y=0 so:

0=-5(x+5)^2+80  add 5(x+5)^2 to both sides

5(x+5)^2=80  divide both sides by 5

(x+5)^2=16  take the square root of both sides

x+5=±√16  which is

x+5=±4  subtract 5 from both sides

x=-5±4 so the x-intercepts are:

x=-1 and -9


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