I am a junior in high school and I am having the hardest time with ALGEBRA 3! I didn't even take Algebra 2 and I failed ALgebra 1 the first time! I am doing online schooling at this time and it is really hard without someone explaining it to me...

We are doing Linear Functions and I do not understand how to tell if a table represents a linear function or not can someone please explain this to me??


Thank you so much!

♥♥Kellie♥♥

A linear function is a function in which has a constant rate of change, in this case, a constant slope.

So if the table represents a constant slope throughout, then you have a linear function.

What I'm worried about is that you're taking algebra 3 when you should have retaken algebra 1...

Wish you the best.

To recognize a linear function from a table of data with two columns x and y is that:
for the same increaments of x you get a constant increament in y ( i.e. take x1=2,y1=10,
x2=3,y2=15 , here x changes by 1 and y changes by 5. now if x3=8 and x4=9 x changes by 1 then y4-y3 should be 5 as well
as an equation, linear function has the form y^1=constant * x^1 + another constant

sometimes to understand a linear function you nead to know nonlinear functions:
look at y=2^x +5
when x changes from 2 to 3 ( i.e. xchanges by 1), y changes from 9 to 13 (y changes by 4
when x changes from 10 to 11 (i.e xchanges by 1) but y changes from 1029 to 2053, ( y changes by 1024)
this is the exponential function.