Question

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

Answer 1

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

Answer 2

Answer:

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

D) (-6, -5)

Step-by-step 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:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here we have:

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

Hence, equation of line is:

$y-4=\dfrac{1-4}{-2-0}\times (x-0)\\\\y-4=\dfrac{-3}{-2}\times x\\\\y-4=\dfrac{3}{2}x\\\\y=\dfrac{3}{2}x+4--------------(1)$

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.

$y=\dfrac{3}{2}\times 5+4\\\\y=\dfrac{23}{2}\neq 12$

Hence, option A is incorrect.

B)

(6,-4).

When x=6.

$y=\dfrac{3}{2}\times 6+4\\\\y=13\neq -4$

Hence, option B is incorrect.

C)

(-3,-1)

when x=-3

$y=\dfrac{3}{2}\times (-3)+4\\\\y=\dfrac{-1}{2}\neq -1$

Hence, option C is incorrect.

D)

(-6,-5)

when x=-6

$y=\dfrac{3}{2}\times (-6)+4\\\\y=-9+4\\\\y=-5$

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)