Question

Look at the cordinates below and write a linear equation (1,2) and (5,10)

Answer 1

Given:

The cordinates are (1, 2) and (5, 10).

Aim:

We need to find the equation of the line.

Step-by-step explanation:

Consider the line equation.

`y=mx+b`

Substitute x=1 and y=2 in the equation.

`2=m\left(1\right)+b`
`b=2-m`

Substitute x=5 and y=10 in the line equation.

`10=m\left(5\right)+b`

`10=5m+b`

Substitute b=2-m in the equation to find the values of m.

`10=5m+2-m`

Solve for m.

`10-2=5m-m`

`8=4m`
`m=(8)/(4)`
`m=2`

We get m=2.

Substitute m=2 in the equation b =2-m to find the values of b.

`b=2-2=0`

We get b=0.

Substitute m=2 and b=0 in the line equation.

`y=2x+0`

Final answer:

The line equation is

`y=2x`