Question

Select all of the equations that represent linear relationships. 5+ 2y = 13 y = x² +7= y-5=2(x - 1) A/N=x+7 X = -4

Answer 1

y-5=2(x-1)

Step-by-step explanation:

let's take a look one by one.

5+2y=13 is not a linear relationship, as there is only one variable.

y=x^2+7 is not a linear relationship, it's quadratic due to the degree.

y-5=2(x-1) is a linear relationship. it forms a line and has two variables.

A/N=x+7 is not a linear relationship. there are three variables.

X=-4 is not a linear relationship. there is only one variable.

Answer 2

The equations that represent linear relationships are 5 + 2y = 13 and x = -4.

Step-by-step explanation:

To identify linear relationships, we need to look for equations that, when simplified, have variables raised to the power of 1 and do not involve any other powers.

a) 5 + 2y = 13 is a linear equation. When solved for y, it simplifies to y = 4, indicating a linear relationship where y is directly proportional to a constant.

b) y = x² + 7 is not a linear equation because of the x² term. The presence of a squared term makes it a quadratic equation, indicating a non-linear relationship.

c) y - 5 = 2(x - 1) is a linear equation. When expanded and simplified, it becomes y = 2x - 3, showing a linear relationship between x and y.

d) N = x + 7 is a linear equation. When solved for x, it simplifies to x = N - 7, representing a linear relationship between N and x.

e) x = -4 is a linear equation, representing a vertical line passing through the point (-4, 0). It is a direct relationship where x is fixed at -4.

Understanding the characteristics of linear equations, such as having variables raised to the power of 1 and not involving other powers, is essential for recognizing and interpreting linear relationships in mathematical expressions. In this case, the selected equations 5 + 2y = 13 and x = -4 meet these criteria, confirming their linearity.