Question

The equation y = x + 1 defines the relationship between x and y, where x is the input and y is the output. Which statements about the graph of this relationship are true? Select two that apply.
A.The graph is a curved line.
B.The graph is a straight line.
C.the graph is a vertical line.
D.The graph represents a function.
E.The graph has no negative outputs.
F.The graph passes through the origin.

Answer 1

Hey there!

Let's go through all of our options.

A) It's defintely not curved; it's written in slope intercept form and is indeed a straight line.

B) Yes, the graph is a straight line. Although it's at an angle, it has no curves or flaws, and is completely straight.

C) The graph is not vertical. It has a y intercept and slope and therefore isn't. That's because it has a rate of change, and it crosses the y axis at some point depending on the slope, or rise over run. Vertical lines really don't have that.

D) Yes, the graph is a function. This is because it does not have two x values for one y, and does not fail the straight line test, which states that you can place a straight line anywhere on the graph and it can only go through one point.

E) This is false. If we put in -5 as our input, we add 1 and get -4, which is a negative output. Your output here depends on the input you put in, and the sign usually remains considering it's +1.

F) This graph does not pass through the origin. This is because the origin has a point at 0,0 and since it's x+1, it would be 0,1 instead because your output is adding one to that 0.

Hope this helps!

Answer 2

The graph is a straight line because y = x + 1 has a slope of 1 (and it's not changing so it can't be curved, neither is it ∞ so it can't be vertical).  This graph does not pass through the origin because it has a + 1 at the end. It is a function because no input matches to 2 different outputs. It also has negative outputs because what if x was -50.

All in all, your answers are B and D.