linear equation.?

Question

how can you tell an equation is linear.
pls give example

Answer 1

It does not involve any products or roots of variables. All variables occur only to the first power and do not appear as arguments of trigonometric, logarithmic or exponential functions. The following are linear equations:
x + 3y = 7
x - 2y +3z =0
[1/2]x =5

The following are not linear equations:
x + 3y^2=5
x + y + xy =75
sinx + y = 0

Answer 2

A linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. Such an equation is equivalent to equating a first-degree polynomial to zero. These equations are called "linear" because they represent straight lines in Cartesian coordinates. A common form of a linear equation in two variables is y = mx + b, (e.g. y = 3x + 5). In this form, the value m will determine the slope or gradient of the line; and the value b will determine the point at which the line crosses the y-axis.

Answer 3

Because the highest "order" of the independent variable is one.

y = f(x) = 2a - 3x + 7b

"y" is shown to be a function of only "x" ----- f(x)

Therefore the "a" and "b" are just nameless constants and of NO concern in this equation. Most importantly note the 'order' of "x". In other words, note that x is raised to the first power, which means there is no exponent.

This indicates that it's linear.

A simpler function would be: y = f(x) = x

If it were y = f(x) = x^2 then it would NOT be linear.

The plot of a 'linear; function plots as a straight line...always.

Hope this helps you. :)

Answer 4

If your equation can be written in the form Ax + By = C, where A B and C are integers, it is a linear equation.

Answer 5

y=5 is a horizontal line each time y= a relentless it extremely is a relentless line(horizontal) vertical is whilst x= a relentless diagonal line is a linear equation with slope coated (different than 0) y=mx+b is the linear equation

Answer 6

an equation is linear if the following 2 conditions holds :

1) if u and v are solutions of the equation then u+v is also a solution of the equation.

2) if u is a solution and k a scalar then ku is also a solution.

hopes this helps.

for funtion idem dito :
f(u+v) = f(u) + f(v)
and f(k.u) = k.f(u)

the f is a liniair function

Answer 7

In linear eqns, the only exponent of any variables is 1. Ex:
y=2x+3
z=4y+5x-6

Answer 8

The variables are raised only to the first power.

This produces a graph which is a straight line.

Hence the term 'linear'