Question

1. Create a linear expression and create equivalent expression. 2. Explain how you know your expression is equivalent to the original.

Answer 1

Use a line already drawn on a graph and its demonstrated points before creating a linear equation. Follow this formula in making slope-intercept linear equations: y = mx + b. Determine the value of m, which is the slope (rise over run). Find the slope by finding any two points on a line.

Answer 2

Answer: The linear expression is x+4.

Step-by-step explanation: We are given to create a linear expression and also to create equivalent expressions and explain your other expressions are equivalent to the original one.

Let the linear expression be

`m=x+4.`

And also, equivalent expressions be

`n=(x^2+6x+8)/(x+2),\\\\o=(x^2-16)/(x-4),\\\\p=(x^2+x-12)/(x-3).`

Since,

`n=(x^2+6x+8)/(x+2)=((x+4)(x+2))/(x+2)=x+4=m,\\\\o=(x^2-16)/(x-4)=((x+4)(x-4))/(x-4)=x+4=m,\\\\p=(x^2+x-12)/(x-3)=((x+4)(x-3))/(x-3)=x+4=m.`

Thus, these three expressions 'n', 'o' and 'p' are equivalent to the original expression 'm'.