Question

Answer this please !

Answer 1

slope = 6

Explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

`(a)/(2)` = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

`(b)/(2)` = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m =
`(-12-(-6))/(1-2)` =
`(-12+6)/(-1)` =
`(-6)/(-1)` = 6

Answer 2

6

Explanation:

`(y)/(2) =x^(2) -7`

`(a)/(2) =2^(2) -7`

`(a)/(2) =-3`

`a=-6`

`(b)/(2) =1^(2) -7`

`(b)/(2) =-6`

`b=-12`

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

`-6=2m+b`

`-12=m+b`

`-24=2m+2b`

`18=-b`

`b=-18`

`-12=m-18`

`m=6`

Therefore, the slope of line l is 6.