Answer :

To determine which equation represents a linear function, we need to understand the characteristics of linear functions. A linear function is a function whose graph is a straight line. This can be expressed in the standard form [tex]y = mx + b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

Let's examine each option:


  • a. [tex]Y = x[/tex]: This is a linear function because it can be written in the form [tex]y = 1x + 0[/tex], where the slope [tex]m = 1[/tex] and the y-intercept [tex]b = 0[/tex].


  • b. [tex]Y = 4x^2[/tex]: This is not a linear function because it involves [tex]x^2[/tex], making it a quadratic function, which graphs as a parabola, not a straight line.


  • c. [tex]Y = \frac{3}{4}x + 3[/tex]: This is a linear function in standard form where the slope [tex]m = \frac{3}{4}[/tex] and the y-intercept [tex]b = 3[/tex].


  • d. [tex]Y = \frac{2}{x}[/tex]: This is not a linear function because it involves division by [tex]x[/tex], resulting in a rational function, which graphs as a hyperbola.



Based on these evaluations, the equations [tex]Y = x[/tex] and [tex]Y = \frac{3}{4}x + 3[/tex] both represent linear functions. Since the most straightforward answer following the standard linear equation format [tex]y = mx + b[/tex] is option c. [tex]Y = \frac{3}{4}x + 3[/tex], we will choose that as the clearest example of a linear function.

Thanks for taking the time to read Which represents a linear function a Y xb Y 4x²c Y 3 4x 3d Y 2 x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada