Question

find the value of a if the line 5 Y is equal to ax + 10, will pass through the 2 , 3 or 1 , 1

Answer 1

$\textbf{Answer :}$

The given straight line is

5y = ax + 10 ...(i)

When the line (i) will pass through the point (2, 3),

5 (3) = a (2) + 10

➩ 15 = 2a + 10

➩ 2a = 15 - 10

➩ 2a = 5

➩ a = $\frac{5}{2}$

Now, putting a = $\frac{5}{2}$ in (i), we get the required straight line as

5y = $\frac{5}{2}$x + 10

➩ 10y = 5x + 20

➩ $\textbf{2y = x + 4}$

Again when the line (i) passes through the point (1, 1),

5 (1) = a (1) + 10

➩ 5 = a + 10

➩ a = 5 - 10

➩ $\textbf{a = - 5}$

Now, putting a = - 5 in (i), we get the required line as

5y = (- 5)x + 10

➩ y = - x + 2

➩ $\textbf{x + y = 2}$

$\textbf{Hope it helps!}$

Answer 2

Solution :

    The given line is 5y = ax + 10 .....(i)

CASE - 1

When the line (i) will pass through the point (2, 3), from (i), we will get

    5 (3) = a (2) + 10

    ⇒ 2a = 15 - 10

    ⇒ 2a = 5

    ⇒ a = 5/2

    ∴ a = 5/2

CASE - 2

When the line (i) will pass through the point (1, 1), from (i), we will get

    5 (1) = a (1) + 10

    ⇒ a = 5 - 10

    ⇒ a = - 5

    ∴ a = - 5

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