In the x-y coordinate plane, the graph of x=y^2-4 intersects line l at (0,p) and (5,t)? What is the greatest possible value of the slope of l?

Semaj Benjamin

Semaj Benjamin

Answered question

2023-03-17

In the x-y coordinate plane, the graph of x = y 2 - 4 intersects line l at ( 0 , p ) and ( 5 , t ) ? What is the greatest possible value of the slope of l?

Answer & Explanation

Razorel1l1

Razorel1l1

Beginner2023-03-18Added 6 answers

Given:
Points ( 0 , p ) and ( 5 , t ) lie on the curve x = y 2 - 4
A line through the points has the following slope:
m = t - p 5 - 0
m = t - p 5
We find that both t and p have the following two possible values when we solve for them:
0 = p 2 - 4 and 5 = t 2 - 4
p 2 = 4 and t 2 = 9
p = ± 2 and t = ± 3
The greatest value will occur when, t is positive and p is negative:
m = 3 - ( - 2 ) 5
m = 5 5
m = 1

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