Respuesta :
The linear function that passes through the point (3,6) is given by: Option C: [tex]y = 2x[/tex]
How to know if a point lies in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Checking all the options to see if (3,6) lies on them:
- Case 1: [tex]y = 3x + 6[/tex]
Usually points are of the form (x,y). Thus, we have: (x,y) = (3,6) means x = 3, and y = 6.
Putting these values in the equation, we get:
[tex]y = 3x + 6\\6 = 3(3) + 6\\6 = 9 + 6\\6 = 15[/tex]
This is wrong. Thus, the point (3,6) doesn't satisfy this equation, and therefore, doesn't lie on its graph.
- Case 2: [tex]y = 6x - 3[/tex]
Putting x = 3, y = 6 in this equation, we get:
[tex]y = 6x - 3\\6 = 6(3) - 3\\6 = 18 - 3 \\6 = 12[/tex]
This is wrong. Thus, the point (3,6) doesn't satisfy this equation, and therefore, doesn't lie on its graph.
- Case 3: [tex]y = 2x[/tex]
Putting x = 3, y = 6 in this equation, we get:
[tex]y = 2x\\6 = 3(2)\\6 = 6[/tex]
This is correct. Thus, the point (3,6) satisfy this equation, and therefore, lies on its graph.
Thus, the linear function that passes through the point (3,6) is given by: Option C: [tex]y = 2x[/tex]
Learn more about points lying on graph of a function here:
https://brainly.com/question/1979522
