Find a formula for the given linear function. The graph of h intersects the graph of y=x^2 at x= -4 and x=9?

Question

Find a formula for the given linear function. The graph of h intersects the graph of y=x^2 at x= -4 and x=9?

Answer 1

The linear function is y = kx + a

x= -4 y=16:    16 = - 4k + a

x =9  y =81:    81 =  4k + a

=> f = 97/2 = 48.5   k = 65/8 = 8.125

y =8.125x + 48.5

Answer 2

points of intersection are (-4,16) and (9,81).

Now use the twopoint form,

y-16=(81-16)/(9+4)(x+4)

y-16=5(x+4)

Answer 3

First, find y when x=-4 and when x=9:

y=x^2, so when x=-4 y=16 and when x=9, y=81

this gives you two points, (-4,16) and (9,81).  Find the equation of the line with these two points.

The slope is the difference of the y's over the difference in the x's:

Difference of the y's: 81-16=65

Difference of the x's: 9-(-4)=13

Slope=65/13=5

Using the point-slope form,

(y-16)=5*(x-(-4))

y-16=5*(x+4)

y-16=5x+20

y=5x+36 is the euqtion of the line

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Answer 4

The two points of intersection are (-4,16) and (9,81)

So slope = (81-16)/(9-(-4)) = 65/13 = 5

so equation is y = 5x + b

Since line goes through (-4,16) we have:

16 = 5(-4) + b --> b = 36

So final equation is y = 5x+36

Answer 5

The linear function intersects at the points (-4,16) and (9,81)

So, we find an equation that goes through both points

Slope between points = 65/13 = 5

y = 5x +___

81 = 5(9) + ___

81 = 45 + 36

y = 5x + 36