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
[tex]m=x+4.[/tex]
And also, equivalent expressions be
[tex]n=\dfrac{x^2+6x+8}{x+2},\\\\o=\dfrac{x^2-16}{x-4},\\\\p=\dfrac{x^2+x-12}{x-3}.[/tex]
Since,
[tex]n=\dfrac{x^2+6x+8}{x+2}=\dfrac{(x+4)(x+2)}{x+2}=x+4=m,\\\\o=\dfrac{x^2-16}{x-4}=\dfrac{(x+4)(x-4)}{x-4}=x+4=m,\\\\p=\dfrac{x^2+x-12}{x-3}=\dfrac{(x+4)(x-3)}{x-3}=x+4=m.[/tex]
Thus, these three expressions 'n', 'o' and 'p' are equivalent to the original expression 'm'.
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.
