Question

Help with this equation please

Answer 1

`y=-(2)/(3)x+6`

Explanation:

Let the equation of the line representing the given table is,

y = mx + b

Here, m = slope of the line

b = y-intercept

From the given table,

Since, slope of the line passing through
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)`

Therefore, slope of the line passing through (3, 4) and (4,
`(10)/(3)`) will be,

m =
`(4-(10)/(3) )/(3-4)`

=
`((12-10)/(3))/(3-4)`

=
`-(2)/(3)`

Therefore, equation of the line will be,

`y=-(2)/(3)x+b`

Since, this line passes through a point
`(1, (16)/(3))`,

By satisfying the equation with the given point,

`(16)/(3)=-(2)/(3)(1)+b`

`b=(16)/(3)+(2)/(3)`

`b=(18)/(3)`

`b=6`

Therefore, equation of the line will be,

`y=-(2)/(3)x+6`