Which equation represents a proportional relationship between the x and y values?

a) y = 2

b) y = 14x + 1

c) y = x − 4

d) y = −2x

D)

Step-by-step explanation:

A linear relationship is of the form , where, is the slope and is the y-intercept (constant).

For a proportional relationship, the value of and thus it is of the form

Let us check each option and express it in the form above.

Option A:

This can be written as . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.

Option B:

Here, . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.  

Option C:

Here, . So, .

Since, b \ne 0, therefore, it is not a proportional relationship.  

Option D:

This can be rewritten as

There is no y-intercept on this. So,

Since,, therefore, it is a proportional relationship.

Therefore, the correct option is D.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!