Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
