Question

Which equation could have been used to create this table?

Answer 1

Answer:

y = 3x

Step-by-step 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

Answer 2

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3$

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