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Angle between Two Lines

If a∗ b=ab+...

Question

If $a * b = a b + a + b$ , draw the graph of $y = 3 * x + 1 * 2$ .

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Solution

Given : $a * b = a b + a + b$ ....... $(i)$
Consider, $y = 3 * x + 1 * 2$
$= 3 x + 3 + x + 1 \times 2 + 1 + 2$ ......... From $(i)$
$= 4 x + 8$
So, the equation we get is $y = 4 x + 8$
Let's assign some values to $x$ and get the values for $y$
$x$ $- 2$ $- 1$ $0$ $1$
$y$ $0$ $4$ $8$ $12$
Plot these points on the graph and get the same image as shown above.

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Similar questions

If a * b = ab + a + b, draw the graph of y = 3 * x + 1 * 2.

x = 1 + a + a^{2} + a^{3} + . . .

y = 1 + b + b^{2} + b^{3} + . . . .

, then show that

1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . . = \frac{x y}{x + y - 1}

x = 1 + a + a^{2} + . . . \infty, (| a | < 1), y = 1 + b + b^{2} + . . . \infty, (| b | < 1),

z = 1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . . \infty

Q. Use the table given below to draw the graph.

$x$	$- 5$	$- 1$	$3$	$b$	$13$
$y$	$- 2$	$a$	$2$	$5$	$7$

From your graph, find the values of

^{'} a^{'}

^{'} b^{'}

.
State a linear relation between the variables

x

y

x = 1 + a + a^{2} + a^{3} + . . . . . \infty

y = 1 + b + b^{2} + b^{3} + . . . . . \infty

1 + a b + a^{2} b^{2} + . . . . \infty = \frac{x y}{x + y - 1}

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