Question

Which equation could have been used to create this table?

A. y = x + 3

B. y = 4x

C. y = 3x

D. y = x + 2

Answer 1

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (1, 3) and (2, 6). Substitute:

`m=(6-3)/(2-1)=(3)/(1)=3`

Therefore we have:

`y=3x+b`

Put the coordinates of the point (1, 3) to the equation and calculate a value of b:

`3=3(1)+b`

`3=3+b` subtract 3 from both sides

`0=b\to b=0`

Answer: y = 3x + 0 = 3x

Answer 2

y = 3x

Explanation:

(1,3) (2,6)

The first step is to find the rate of change ( or slope)

m = (y2-y1)/(x2-x1)

m = (6-3)/(2-1)

m = 3/1

m = 3

Then we need to use the point slope form of the equation of a line

y-y1 = m(x-x1)

y-3 = 3(x-1)

Distribute the 3

y-3 = 3x-3

Add 3 to each side

y-3+3 = 3x-3+3

y = 3x