Question

which equation represents the linear relationship between the x - values and the y - values in the table?

x	y
-1	-11
1	1
3	13
5	25

f y = 2x + 12
g y = 5x - 6
h y = 6x - 5
j y = -x - 11

Explanation:

Step1: Select a point from the table

Let's take the point $(x = 1,y = 1)$.

Step2: Substitute into option F

Substitute $x = 1$ into $y=2x + 12$, we get $y=2\times1+12=14
eq1$.

Step3: Substitute into option G

Substitute $x = 1$ into $y = 5x-6$, we get $y=5\times1 - 6=-1
eq1$.

Step4: Substitute into option H

Substitute $x = 1$ into $y=6x - 5$, we get $y=6\times1-5 = 1$.

Step5: Check another point

Let's take $x = 3,y = 13$. Substitute into $y=6x - 5$, we get $y=6\times3-5=18 - 5=13$.

Answer:

H. $y = 6x-5$