Question

Which coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function?

A) (5, 12)
B) (6, -4)
C) (-3, -1)
D) (-6, -5)

Answer 1

D) (-6, -5) is the answer. ope it helps!

Answer 2

Hence, the coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function is:

D) (-6, -5)

Explanation:

We are given coordinates of the linear function as:

{(0,4),(-2,1),(-4,-2)}

We know that we can find the linear equation with the help of two points.

Consider two points:

(0,4) and (-2,1).

The equation of a line passing through two points (a,b) and (c,d) is given by:

`y-b=(d-b)/(c-a)* (x-a)`

Here we have:

(a,b)=(0,4) and (c,d)=(-2,1)

Hence, equation of line is:

`y-4=(1-4)/(-2-0)* (x-0)\\\\y-4=(-3)/(-2)* x\\\\y-4=(3)/(2)x\\\\y=(3)/(2)x+4--------------(1)`

Hence the line has slope 3/2 and y-intercept as 4.

Now we are asked to find out which point passes through the given linear function:

i.e. we will put x-value in the equation and check for which y-values hold true, the point will lie on the line segment.

A)

(5,12)

we will put x=5 in equation (1) and check whether y=12 or not.

when x=5.

`y=(3)/(2)* 5+4\\\\y=(23)/(2)\\eq 12`

Hence, option A is incorrect.

B)

(6,-4).

When x=6.

`y=(3)/(2)* 6+4\\\\y=13\\eq -4`

Hence, option B is incorrect.

C)

(-3,-1)

when x=-3

`y=(3)/(2)* (-3)+4\\\\y=(-1)/(2)\\eq -1`

Hence, option C is incorrect.

D)

(-6,-5)

when x=-6

`y=(3)/(2)* (-6)+4\\\\y=-9+4\\\\y=-5`

Hence option D is correct.

Hence, the coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function is:

D) (-6, -5)