What is Dx+t=10,for x
1 answer:
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Answer:
The equation represents in R^2 c) a line
The equation represents in R^3 a) a plane
The equation represents in R^3 a) a plane
The equation represents d) a plane
The pair of equations represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , with
∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set we will have only one free variable in R^2 (which is a line in R^2). Therefore,
represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set we will have only two free variables (y and z) and
will represent a plane (which have two dimensions) in R^3.
2) The equation in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
Answer:
a) not proportional
b) proportional; k =
Step-by-step explanation:
a) for any proportional equation, the line must pass through the origin. The equation in a) is y = 4x + 1, and the '+1' is the y-intercept. This means that the line does not pass through the origin, so x and y cannot increase by the same amount (i.e. they are not proportional).
Another way to determine this is is to use the y = kx base. If you have an equation that fits that it's likely proportional.
Here, if the equation was only y = 4x then it'd be proportional because u can see that k = 4. This is not the equation though, and the 4x + 1 doesn't fit to the y = kx formula so it can't be proportional.
b) straight away you can see that there's no 'c' term (y = mx + c) which means the y-intercept is 0, so the line passes through the origin. While this does not immediately mean the line is proportional, you can make sure that it is by checking it fits with the y = kx equation.
y = -(3/5)x fits with y = kx, with k being -3/5