Question

Suppose that the given line has a slope of -2/3 and a y-intercept of (0,5/3). which of the following points is also a solution to the line? select all apply

A. (5,5/3)
B. (1,1)
C. (4,-1)
D. (-3,7)
E. (0,0)

Answer 1

From five given points it is find that points (1 , 1) and (4 , -1) will apply

Explanation:

According to question,

Slop of line (m) =
`(-2)/(3)`

And y-intercept is ( 0,
`(5)/(3)`)

So from above slope and points, the equation of line can be written as

y = mx + c

i.e
`(5)/(3)` =
`(-2)/(3)` x + c

`(5)/(3)` =
`(-2)/(3)` (0) + c

`(5)/(3)` = 0 + c

Or, c =
`(5)/(3)`

A) With points ( 5,
`(5)/(3)` )

At x = 5, y =
`(-2)/(3)` (5) +
`(5)/(3)`

or, y =
`(-10)/(3)` +
`(5)/(3)`

so, y =
`(-5)/(3)`

Hence this points do not apply

B) With points ( 1 , 1 )

At x = 1, y =
`(-2)/(3)` (1) +
`(5)/(3)`

or, y =
`(-2+5)/(3)`

So, y =
`(3)/(3)`

y = 1

Hence this points will apply

C) With points ( 4 , -1 )

At x = 4 , y =
`(-2)/(3)` (4) +
`(5)/(3)`

y =
`(-8+5)/(3)`

y =
`(-3)/(3)`

So, y= -1

Hence this points will apply

D) With points (-3 ,7)

At x = - 3, y =
`(-2)/(3)` (-3) +
`(5)/(3)`

y =
`(14)/(3)`

Hence this point will not apply

E) with points (0 , 0)

At x 0, y =
`(-2)/(3)` (0) +
`(5)/(3)`

Or, y = 0 +
`(5)/(3)`

y =
`(5)/(3)`

Hence this point will not apply

∴ From above five given points it is find that points (1 , 1) and (4 , -1) apply

Answer