I need help with function linear???

Question

Which of these Equations or functions are linear ? yes or no you'll help a lot if you explain me why
Becuase seriously i'm having a lot of problems with them

h(x) =23

y= 2/3x

y=5/x

9-5xy=2

I hope you can help me

Answer 1

Linear functions are called "linear" because they are precisely the functions whose graph in the Cartesian coordiante plane is a straight line."

"Such a function can be written as

f(x) = mx + b,
where m and b are real constants and x is a real variable. The constant m is often called the slope while b is the y-intercept, which gives the point of intersection between the graph of the function and the y-axis. Changing m makes the line steeper or shallower, while changing b moves the line up or down."

Of the above equations which are able to be graphed in a straight line on the Cartesian Coordinate Plane.

f(x) = mx + b

h(x) =23 ; f(x) = 23, this would be a constant function. Since all ordered pairs belonging to f have a y-coordiante of 23, the graph is the horizontal line given by y= 23. Remember, y and f(x) are equivalent, that is , y = f(x).

Any function which can be written in the form f(x) = ax + b, where a and b are real numbers and "a" never equals zero is called a linear function. A linear function can also be written in the form y= mx +b.

y = 2/3x

y = 5/x

9 - 5xy =2

Are the equations a straight line on the Cartesian Plane?

Use the fomula.

Answer 2

h(x) =23 This is a vertical line through the point (23,0). Everywhere on this vertical line, x = 23.

y= 2/3x I assume you mean y = (2/3)x and not 2/(3x). If so this is a straight line with slope = 2/3 and passes through the origin.

y=5/x This is the same as xy = 5 and is a hyperbola. It is not linear.

9-5xy =2
-5xy = -7
xy = 7/5 which again is a hyperbola and is not linear.

The first two problems y varies directly with x and so is linear since x is of degree 1 (not raised to a power greater than 1).

In the last two problems y vaies inversely with x (x is in denominator) and so is non-linear, even though x is of degree 1.

Answer 3

Linear function is a function that fits one of these forms:

f(x)=ax+b
y=ax+b

What this basically means is that for a given X, there is one and ONLY one Y. When you graph them, the line also must be linear. (straight)

h(x) =23
While this is a constant, it is a linear function. For a given value of X, it returns one value of Y. It also fits the format of f(x)=ax + b. a is zero in this case.


y= 2/3x
Did you mean y=(2/3)x or y=2/(3x)?
First is a linear function but the second is not. While there is one to one relationship, second one does not fit the standard form.

y=5/x
Same as above

9-5xy=2
You will need to rewrite this into y= format.
You should end up with y=7/(5x)
So.... it is not a linear function for the same reason as two above.

Answer 4

A function is linear if f(x1 + x2) = f(x1) + f(x2) for every x1 and x2 in its domain. Let's see.

h(x) = 23 a constant function. f(x1 + x2) = 23 < f(x1) + f(x2) = 23 + 23 = 46 So, constant non indentically zero functions are not linear.

y = (2/3)x. f(x1 + x2) = (2/3) (x1 + y2) = 2/3 x1 + 2/3 x2 = f(x1) + f(x2y). So, it's linear. Every function of the form f(x) = mx, m constant, is linear. This is the only kind of continuous linear functions from R to R.

y = 5/x. f(x1 + x2) = 5/(x1 + x2) and f(x1) + f(x2) = 5/x1 + 5/x2 = 5 (1/x1 + 1/x2) = 5 xy/(x1 + x2). It's clear that, if x1 x2 <>1, then f(x1 + x2)) <> f(x1) + f(x2). Not linear.

9-5xy=2, the same as y = 7/(5x). The same reasoning of the previous example. Not linear.

Answer 5

Linear equations are those of the form: y = a + bx

The first is linear: y = h(x), a = 23, b = 0
The second is linear: a = 0, b = 2/3
The third and fourth are nonlinear.