Question

which show a linear function? select 2. select all correct options

Explanation:

Step1: Recall the definition of a linear function

A linear function has the form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept) and its graph is a straight line. Also, it must pass the vertical line test (each \( x \)-value has exactly one \( y \)-value) and be a straight line (not a curve).

Step2: Analyze the first graph (green - colored)

The first graph (green background) is a V - shaped graph. This is the graph of an absolute - value function (\( y=\vert x\vert\) shifted or not), which is not a linear function (it has a "corner" and is not a straight line with a constant slope everywhere). Wait, no, wait. Wait, actually, the first graph: Wait, no, let's re - examine. Wait, the second graph (blue background) is a straight line passing through the origin, so it has the form \( y = mx\) (a linear function with \( b = 0\)). The fourth graph (blue - colored, "Applicants Accepted" graph) is a straight line, so it represents a linear function (since it's a straight line and will satisfy \( y=mx + b\)). The third graph (orange background) is a curve (a parabola - like or a cubic - like curve), so it's not a linear function. Wait, the first graph: Wait, the first graph (green) is a V - graph, which is not linear. The second graph (blue) is a straight line, so it's linear. The fourth graph (the one with "Applicants Accepted") is a straight line, so it's linear. Wait, the problem says "Select 2". Let's check again.

Wait, the second graph (blue) is a straight line, so it's a linear function (it has a constant slope, passes the vertical line test). The fourth graph (the one with the axes labeled "Applicants Accepted" and "Applications Received") is a straight line, so it's a linear function. The first graph is a V - graph (absolute value, not linear), the third is a curve (not linear). So the correct ones are the second (blue - colored graph) and the fourth (the graph with "Applicants Accepted" label).

Answer:

The blue - colored graph (the straight line passing through the origin) and the blue - colored graph with "Applicants Accepted" label (the straight - line graph of applicants) are the linear functions. So the two correct options are the second graph (blue background, straight line through origin) and the fourth graph (blue background, "Applicants Accepted" straight - line graph).