Question

The equation of a function is y=2\3x +1\3 find

a] the value of y when'
i] x=-3 ii] x=1 1\2
b] the value of x when
i] y=1 ii] y=-1\6
please help me solve this equation asap i have 100 marks exam tommorow!

Answer 1

a) i) y = - 5/3

ii) y = 4/3

b) i) x = 1

ii) x = -3/4

Explanation:

`y=\frac23x +\frac13`

a) i)
`x=-3`

`\implies y=\frac23(-3) +\frac13\\\\\\\implies y=(-6)/(3) +\frac13\\\\\\\implies y=(1-6)/(3) \\\\\\\implies y=-\frac53`

ii)
`x=1\frac12=\frac32`

`\implies y=\frac23\left(\frac32\right) +\frac13\\\\\\\implies y=(6)/(6)+\frac13\\\\\\\implies y=(3)/(3)+\frac13\\\\\\\implies y=(3+1)/(3)\\\\\\\implies y=\frac43`

b) i)
`y=1`

`\implies \frac23x +\frac13=1\\\\\\\implies \frac23x =1-\frac13\\\\\\\implies \frac23x =\frac23\\\\\\\implies x =1`

ii)
`y=-\frac16`

`\implies \frac23x +\frac13=-\frac16\\\\\\\implies \frac23x =-\frac12\\\\\\\implies x =-\frac12 / \frac23=-\frac12 *\frac32=-\frac34`