How do I write parametric equations of the line 2x+3y=11
1 answer:
This line is in standard form, and the first thing we need to do is convert it into point - slope form or simply isolate y -
2x + 3y = 11, Subtract 2x from either side
3y = - 2x + 11, Divide either side by 3
y = ( - 2x + 11 ) / 3
To derive the parametric equation say x = t -
y = ( - 2t + 11 ) / 3,
or in other words
<u><em>Solution = y = ( 11 - 2t ) / 3</em></u>
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The given <span>expression is 
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So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
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<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>
</span>
So, we have 3 square roots.
The number under a square root sign must be Non negative.
Beside that the denominator must be not equal zero.
For the term ⇒⇒⇒
∴ x > 0 ⇒⇒⇒ x ∈ (0,∞)
For the term ⇒⇒⇒
∴x+1 ≥ 0 ⇒⇒⇒ x ≥ -1 ⇒⇒⇒ ∴ x ∈ [-1,∞)
For the term ⇒⇒⇒
∴ 1-x ≥ 0 ⇒⇒⇒ x ≤ 1 ⇒⇒⇒ x ∈ (-∞,1]
So, The values of x which make the <span>expression well defined
</span>
<span>∴ x ∈ { </span><span>(0,∞) ∪ </span><span>[-1,∞) ∪ </span><span>(-∞,1] }
</span><span>
</span><span>∴ x ∈ [-1,0) ∪ (0,1]
</span><span>
</span><span>OR can be written as ⇒⇒ x ∈ [-1,1] - {0}
</span>