Question

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation:

x	6	– 6
y	–2	6

Draw the graph using the values of x, y as given in the above table. At what points the graph of the linear equation cuts the y-axis

Answer 1

Given, points are (6, –2) and (–6, 6).

Let the linear equation y = mx + c is satisfied by the points (6, –2) and (– 6, 6) then at point (6, – 2)

–2 = 6m + c  .....(i)

And at point (–6, 6), 6 = – 6m + c  ......(ii)

On subtracting equation from equation (i), we get

12m = – 8 

⇒ m = ${\displaystyle \frac{-8}{12}}$

⇒ m = ${\displaystyle -\frac{2}{3}}$

On putting the value of m in equation (i), we get

–2 = ${\displaystyle 6(-\frac{2}{3})+c}$

–2 = – 4 + c

⇒ c = – 2 + 4 

⇒ c = 2

On putting m = ${\displaystyle -\frac{2}{3}}$ and c = 2 in linear equation y = mx + c, we get

${\displaystyle y=-\frac{2}{3}x+2}$

⇒ ${\displaystyle y=\frac{-2x+6}{3}}$

⇒ ${\displaystyle 3y=-2x+6}$

⇒ ${\displaystyle 3y+2x}$ = 6

When the graph of the linear equation

Cuts the y-axis

Then, put x = 0 in equation ${\displaystyle 2x+3y}$ = 6, we get

⇒ ${\displaystyle 2\cdot 0+3y}$ = 6

⇒ ${\displaystyle 3y}$ = 6

∴ y = 2

Therefore, the graph the linear equation cuts the Y-axis at the point (0, 2).