Question

Complete equations describing how x and y are related

Answer 1

Explanation:

if you cannot see directly, you can always use 2 pairs of x,y numbers from the table to create 2 equations and solve for the 2 variables.

we could call them a, b.

the equation is then

y = ax + b

now, let's pick x,y pairs with simple numbers.

like 1,1 and 0,-9

1 = a×1 + b = a + b

-9 = a×0 + b

so, the second one gives us b directly

b = -9

with that we go into the first :

1 = a + -9 = a - 9 | add 9 to both sides

1 + 9 = a - 9 + 9

10 = a

so, our equation is

y = 10x - 9

FYI - how could we see it directly ?

well, we see that when x increases by 1, y increases by 10.

so, we know, a = 10.

and the x=0 point gives us b directly : b = -9.

that's really it (for a line).

Answer 2

The equation repesented in the table is y= 10x - 9

How to complete the equation?

We want to complete the linear equation:

y = ax + b

Where a is the slope and b is the y-intercept.

The y-intercept is the value that the function takes when x = 0, and we can see the pair (0, -9), so the y-intercept is -9

y = ax - 9

Now we can choose any other pair in the table, let's use the next one (1, 1), and replace these values, then we can solve the equation for a.

1 = a*1 - 9

1 + 9 = a

10 = a

The equation is.

y= 10x - 9