Final answer:
All the equations provided are linear, as they follow the form y = mx + b, which is the standard form of a linear equation.
Step-by-step explanation:
In the world of mathematics, particularly in the subject of linear equations, determining whether an equation is linear involves checking if it can be written in the form y = mx + b, where m and b represent numbers and x and y are variables. Linear equations produce straight lines when graphed on a coordinate plane.
The equations given in the question:
- y = 2x + 5
- y = -2x + 5
- y = 1/2x - 5/2
- y = -1/2x - 7/2
are all indeed linear because they each follow the format y = mx + b. The coefficients of x (the slope) vary, and the constant term (the y-intercept) also varies, but the structure of a linear equation remains.