Question

in a certain linear equation, the rate of change of y with respect to x is two. write the equation if the coordinate (0,1) is a solution.

Answer 1

`y=2x+1`

Explanation:

Let the linear equation be
`y=mx +b`.

The slope of a linear equation is the same as the rate of change of that linear linear equation.

The rate of change of y with respect to x is given in the question as 2.

`\implies m=2`

We substitute this slope to obtain the partial equation;

`y=2x+b`

If the coordinate (0,1) is a solution, then it must satisfy this equation.

`\implies 1=2(0)+b`

`\implies 1=b`

The required equation is:

`y=2x+1`