Question

Which statement best explains whether y=2x-3 is a linear function or a nonlinear function?

a. It is a linear function because the graph contains the points 0,-3,1,-1,2,1 , which are on a straight line.
b. It is a nonlinear function because the graph contains the points 0,-3,1,-1,2,1 , which are not on a straight line..
c. It is a linear function because the graph contains the points -3,0,-1,1,1,2 , which are on a straight line.
d. It is a nonlinear function because the graph contains the points -3,0,-1,1,1,2 , which are not on a straight line.

Answer 1

The equation y=2x-3 represents a linear function because it forms a straight line when graphed, as indicated by the points (0, -3), (1, -1), and (2, 1), which align on the same line.

Step-by-step explanation:

The equation y=2x-3 is a linear function because it can be written in the form y = a + bx, where a is the y-intercept and b is the slope of the line. When plotted on a graph, the points given, such as (0, -3), (1, -1), and (2, 1), do form a straight line. Therefore, the correct statement is: It is a linear function because the graph contains the points 0,-3,1,-1,2,1 , which are on a straight line. The slope of this line is 2, meaning for every increase of 1 on the horizontal axis (x), there is a rise of 2 on the vertical axis (y), and it crosses the y-axis at -3 (the y-intercept).