Please, I need help with these two problems..

Question

What is a linear equation?

 

Is the given equation a linear equation? If not, explain why not.

 

1.) x⁴-1=0

 

 

2.) 3(4x-9)+7(2x+5)=15

Answer 1

A linear equation has a degree of one, the only exponent is 1.

 

1.) has an exponent of 4. It is not linear

2.) has only the exponent 1 (usually not written). It is linear.

Answer 2

A linear equation is any equation of 2 variables that create a straight line when graphed.  An equation can only make a straight line if it manipulates a variable with direct proportions.  In your question #1 the equation can not be linear because the x variable is being manipulated exponentially.  #2 is linear because the variable "x" is only manipulated multiplication and addition.  If you try to graph the first equation you would find that it creates three turns in the graph.  If you look at the second problem there is only one solution.  It creates a point on the graph which can only be concluded into a line (or possibly many lines through that one point.  Therefore it is linear.

 

Hopefully this helps.  If you need further assistance look me up for tutoring.