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:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
(a,b)=(0,4) and (c,d)=(-2,1)
Hence, equation of line is:
[tex]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)[/tex]
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.
[tex]y=\dfrac{3}{2}\times 5+4\\\\y=\dfrac{23}{2}\neq 12[/tex]
Hence, option A is incorrect.
B)
(6,-4).
When x=6.
[tex]y=\dfrac{3}{2}\times 6+4\\\\y=13\neq -4[/tex]
Hence, option B is incorrect.
C)
(-3,-1)
when x=-3
[tex]y=\dfrac{3}{2}\times (-3)+4\\\\y=\dfrac{-1}{2}\neq -1[/tex]
Hence, option C is incorrect.
D)
(-6,-5)
when x=-6
[tex]y=\dfrac{3}{2}\times (-6)+4\\\\y=-9+4\\\\y=-5[/tex]
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)
