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36 votes
36 votes
This shows a linear function.

x y
0 15
1 25
2 35
3 45
4 55
Which equation represents the table?

A.
y = 10x + 15

B.
y = 15x + 10

C.
y = 10x

D.
y = 15x

User Davzaman
by
3.0k points

1 Answer

19 votes
19 votes

Answer:

Option A: y = 10x + 15

Explanation:

Let's find the equation in the form of y=mx+b that fits the data. m is the slope and b is the y-intercept (the value of y when x=0). Slope, m, the the Rise/Run of the line. It can be found by taking any two points from the table. Let's choose (0,15) and (2,35), although any two will work.

x y

0 15

1 25

2 35

3 45

4 55

(0,15) (2,35)

The Rise is the change in y: (35 - 15) = 20.

The Run is the change in x for the same points: (2 - 0) = 2

The slope is the Rise/Run = (20/2) or 10.

The equation has the form y = 10x + b.

Let's find b. Just enter any of the points in the above equation and solve for b. I'll choose (3,45).

y = 10x + b

45 = 10*(3) + b

b = 45 - 30

b = 15

[Note: since b is the value of y when x equals zero, we really didn't need to calculate b as we just did. There is a data point already that tells us the value of y when x = 0: (0,15)]

The equation is y = 10x + 15

Option A: y = 10x + 15

User Daniel Lavoie
by
3.4k points