Question

Find the equation of the linear function represented by the table below in slope-intercept form

Table to Linear Equation
x y
1 0
2 2
3 4
4 6

Answer 1

`\huge\boxed{y=2x-2}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

The formula of a slope:

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

(x₁; y₁); (x₂; y₂) - points on a line

From the table we have

`(1,\ 0)\to x_1=1;\ y_1=0\\\\(2,\ 2)\to\ x_2=2;\ y_2=2`

Substitute:

`m=(2-0)/(2-1)=(2)/(1)=2`

Put the value of a slope and coordinates of the point (1, 0) to the equation of a line:

`0=2(1)+b`

`0=2+b` subtract 2 from both sides

`-2=b\to b=-2`

Finally we have:

`y=2x-2`