Question

Which equation describes the function shown on the graph?

Answer 1

Answer:

The answer is B.

Step-by-step explanation:

Recall that lines are one of the three undefined terms in geometry, the other two being points and planes. If I had two, I would describe it as a "one-dimensional figure infinitely pointing in both of its directions", but that definition in itself is hard to grasp.

The good thing about undefined terms, though, are that they're easy to describe. Specifically, lines have two key attributes: the slope and the y-intercept.

Slope is "a number that describes both the direction and the steepness of [a] line". It's denoted by m, and it's usually called "rise over run" because slope is also the relationship between the vertical compoenent y and the horizontal component x.

The y-intercept is "the point where [a] line intercects the y-axis". Plain and simple. It also describes the position of a line, and it is denoted by b.

So, we know what slope and the y-intercept are, but how does this help us solve the problem?

Well, we are provided a graph, so let's make sense of the problem.

A line is defined by the slope and the y-intercept, which is why we always write the equation in slope-intercept form (y = mx + b). But this must mean a line must have a unique m and b as well!

So, let's start with b (the y-intercept). The line intersects the y-axis where the 2 margin is, so I can already say that the y-intercept is (0,2). We already have one piece of the puzzle filled: y = mx + 2. We can already rule out A and D.

Now let's find m. Remember that slope is "rise over run". Also, two points can always form a line. This means that at one point, I can move both vertically and horizontally to the next point of the line and use that to write the slope! So let's do that.

From the y-intercept (0, 2), I can move -1 units up and 5 units right to reach the next point on the line, (5,1). For simplicity's sake, we'll just say that rise is y, run is x, and m = y/x. This means that m = -1/5, which is our slope. We can rule out C.

Therefore, our answer is B.