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.

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$$m=\frac{8}{4}$$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

$y=2x$