Exponents relating to linear equations- help

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SUMMARY

The discussion centers on finding the equation of a line that passes through the points (1, π) and (π², π⁴). The user initially struggled with calculating the gradient using the formula m = (y₂ - y₁) / (x₂ - x₁), specifically substituting the values π⁴ - π² and π² - 1. Ultimately, the correct gradient was determined to be m = π² - 3, leading to the final equation of the line as y = π²x.

PREREQUISITES
  • Understanding of linear equations and the slope-intercept form (y = mx + c).
  • Familiarity with basic calculus concepts, particularly gradients.
  • Knowledge of the mathematical constant π and its properties.
  • Ability to perform algebraic manipulations involving exponents.
NEXT STEPS
  • Study the derivation and applications of the slope-intercept form of linear equations.
  • Learn about the properties and applications of the mathematical constant π in various contexts.
  • Explore techniques for solving problems involving gradients and slopes in coordinate geometry.
  • Practice algebraic manipulation of equations involving exponents and roots.
USEFUL FOR

Students studying algebra, mathematics educators, and anyone interested in understanding linear equations and their applications in geometry.

cmaro
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So I need to find the equation of the line passing through (1,∏) (∏₂,∏⁴) sorry, the two would only do sub script not super script but does represent squared.

So I had to find the gradient first, so that I could then sub that along with x and y into y=mx+c but I got stuck trying to find the gradient because there is pi4-pi2 / pi2-1.

How do i figure this out? i tried two things and ended up with pi - 1/pi and then pi2-3.. neither of these seem like gradients?
 
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never mind! i figured it out- it was m= pi2-3, and i ended up with an answer of y=pi2(x) which was correct! :)
 

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