The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation x=6 y=-2 and x=-6 y=6
Answers
Given : x=6 y=-2 and x=-6 y=6 lies on a line
To find : a linear equation
Solution:
Let say linear Equation is
y = mx + c
x = 6 & y = - 2 satisfy this
=> -2 = 6m + c Eq1
x = -6 & y = 6 satisfy this
=> 6 = -6m + c Eq2
Eq 1 + Eq 2
=> 4 = 2c
=> c = 2
=> -2 = 6m + 2
=> -1 = 3m + 1
=> m = - 2/3
y = (-2/3)x + 2
=> 3y = -2x + 6
=> 2x + 3y = 6
2x + 3y = 6 is the linear equation
Another method
x=6 y=-2 and x=-6 y=6 are two point on line
slope = (6 - (-2)) /( -6 - 6) = 8 /(-12) = -2/3
y - (-2) = (-2/3) (x - 6)
=> y + 2 = (-2x + 12)/3
=> 3y + 6 = -2x + 12
=> 2x + 3y = 6
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Step-by-step explanation:
hope it will help you.
ans :2x+3y=6
