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

Draw the graph using the values of x, y as given in the above table.
At what points the graph of the linear equation
(i) cuts the X-axis ? (ii) cuts the Y-axis ?

Explanation

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
and at point (-6, 6), 6= - 6m + c
On subtracting Eq. (ii) from Eq. (i), we get
`12 m= - 8 implies m= (-8)/(12) implies m = - (2)/(3)`
On putting the value of m in Eq. (i). we get
`-2=6(-2//3)+c`
`implies " " -2= - 4+ c implies c = -2+4 implies c=2`
On putting `m= - (2)/(3)` and c=2 in linear equation y= mx+ c we get

`y= - (2)/(3)x+2`
` implies y=(-2x+6)/(3)`
`implies 3y = - 2x+6`
`implies 3y+2x= 6`
When the graph of the linear equation
(i) Cuts the X-axis
Then, put y=0 in equation 2x+3y=6, we get
2x+3.0=6
`implies 2x=6`
`therefore " " x=3`
When the graph of the linear equation
(ii) Cuts the Y-axis
Then, put x=0 in equation 2x+3y=6, we get
`implies " " 2.0+3y=6`
`implies " " 3y=6`
`therefore " " y=2`
Therefore, the graph the linear equation cuts the X-axis at the point (3, 0) and the Y-axis at the point (0, 2).