Question

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

Draw the graphs 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.

Answer 1

slope=(-2-6)/(6--6)=-8/12=-2/3
use point slope formula
y+2=-2/3(x-6)
y=-2/3x + 2. in slope intercept

I) cuts x axis at (-4/3,0)
I) cuts y axis at (0,2)

Answer 2

Explanation:

Given are two points on a straight line.

(since x and y are thought to satisfy a linear equation. )

The two points are (x,y) = (6,-2) (-6,6)

Use the two point formula for finding equation

Two point formula is

`(y-y_1)/(y_2-y_1)= (x-x_1)/(x_2-x_1)`

Substitue the values to get

`(x-(-6))/(6-(-6)) =(y-6)/(-2-6) \\x+6 =(12)/(-8)(y-6) \\-2x-12=3y-18\\2x+3y=6`

is the equation

This can also be written in intercept form as

`(x)/(3) +(y)/(2) =1`

Hence x intercept = 3 and y intercept = 2