Question

if point (10,0) and (0,8) are on the graph of equation ax + by = 40. find value of a & b​

Answer 1

Given :-

• Two points (10, 0) and (0,8) are on the equation of the line ax + by = 40.

To Find :-

• Value of a and b.

Solution :-

The equation of a line is given as,

• ax + by = 40

There are two points which satisfy the given equation of line as (10, 0) and (0,8)

Putting the value of x and y from the first point in the equation, we get

⇒ a(10) + b(0) = 40

⇒ 10a = 40

⇒ a = 4

Now, Putting the value of x and y from the second the point in the equation, we get

⇒ a(0) + b(8) = 40

⇒ 8b = 40

⇒ b = 5

Hence, The value of a and b are 4 and 5 respectively.

Some Information :-

• The point on a line satisfies the equation of that line.

• The slope of a line can be found in the following way when the two points on the line are given,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Answer 2

${\pmb{\sf{\underline{Given \; that...}}}}$

• Point (10,0) and (0,8) are on the graph of equation ax + by = 40.

${\pmb{\sf{\underline{To \; find...}}}}$

• Value of a and b

${\pmb{\sf{\underline{Solution...}}}}$

• Value of a = 4
• Value of b = 5

${\pmb{\sf{\underline{Full \; Solution...}}}}$

~ As it is given line as ax + by = 40 and point (10,0) and (0,8) are on the graph of equation ax + by = 40. Firstly let us put 10 and 0 as x and y respectively in the equation ax + by = 40

${\sf{:\implies ax + by = 40}}$

${\sf{:\implies a(10) + b(0) = 40}}$

${\sf{:\implies a \times 10 + b \times 0 = 40}}$

${\sf{:\implies 10a + 0 = 40}}$

${\sf{:\implies 10a = 40}}$

${\sf{:\implies a = 40/10}}$

${\sf{:\implies a = 4}}$

Henceforth, we get 4 as the value of a.

~ Now let us put 0 and 8 as x and y respectively in the equation ax + by = 40

${\sf{:\implies ax + by = 40}}$

${\sf{:\implies a(0) + b(8) = 40}}$

${\sf{:\implies a \times 0 + b \times 8 = 40}}$

${\sf{:\implies 0 + 8b = 40}}$

${\sf{:\implies 8b = 40}}$

${\sf{:\implies b = 40/8}}$

${\sf{:\implies b = 5}}$

Henceforth, the value of b is 5.