Is 3x+8y=5 a function? I am thinking yes
the equation describes a function, yes.
if you want to write y as a function of x, then you have to rearrange things a bit:
y = (5-3x)/8
Well, do you know what a function is?
A function is an equation where every input has only one output.
In notation, x is the input. So the question is really asking: "Can x equal anything in following equation which will result in multiple y-values?"
The best way to figure this out is to isolate y:
3x + 8y = 5
3x - 3x + 8y = 5 - 3x
8y = 5 - 3x
y = 5/8 - 3/8x
So, can we get multiple y-values given any x? In this case, the answer is no, so
3x + 8y = 5 is a function.
To determine if the equation 3x + 8y = 5 represents a function, we need to check if each value of x corresponds to exactly one value of y.
First, let's rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we isolate the y term by subtracting 3x from both sides:
8y = -3x + 5
Next, divide both sides of the equation by 8:
y = (-3/8)x + 5/8
Since the equation is now in slope-intercept form, we can see that for each value of x, there is a corresponding value of y determined by the slope (-3/8) and the y-intercept (5/8).
Therefore, the equation 3x + 8y = 5 represents a function.
To determine if the equation 3x + 8y = 5 represents a function, you need to check if there is a unique output (y-value) for every input (x-value).
To do this, we can rearrange the equation in terms of y: 8y = 5 - 3x. Now divide both sides by 8: y = (5 - 3x) / 8.
Since the equation is written in terms of both x and y, we can conclude that it represents a relation between the two variables. However, to determine if it is a function, we need to check if there are multiple outputs (y-values) for the same input (x-value).
One way to determine this is to assign different x-values and see if we get unique y-values. For example, if we let x = 0, then y = (5 - 3(0)) / 8 = 5 / 8. If we let x = 1, then y = (5 - 3(1)) / 8 = 2 / 8 = 1 / 4. Similarly, if we plug in different x-values, we will always get a unique y-value.
Since there is a unique output (y-value) for every input (x-value), we can conclude that the equation 3x + 8y = 5 represents a function.