Question

the graphed system represents the rate at which two trucks are being filled, where x represents the time in minutes and y represents the percentage filled.
which statement is true?

Explanation:

Step1: Analyze the graph's intercepts and slopes

The two lines represent the filling rates of two trucks. Let's assume the equations of the lines. For a line, the slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Looking at the graph, one line has a y-intercept of 50 (when $x = 0$, $y = 50$), and the other has a lower y-intercept (maybe around 20? Wait, actually, at $x = 0$, the first line (steeper) has $y = 50$, the second (less steep) has a lower y-intercept. But they intersect at some point (let's say when $x = -2$? Wait, the x-axis: the intersection point is at $x = -2$? Wait, no, looking at the grid, the intersection is at $x = -2$? Wait, the x-axis has ticks: -10, then -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. So the intersection is at $x = -2$? Wait, no, the lines cross at $x = -2$? Wait, maybe I misread. Wait, the problem is about which statement is true, but since the options aren't given, wait, no, the user's question might be incomplete? Wait, the original problem says "Which statement is true?" but no options are provided. Wait, maybe the user missed including the options. But assuming that the problem is about analyzing the linear systems (graphs of two lines), the discipline is Mathematics (subfield: Algebra, since it's about linear equations and their graphs).

But since the options are missing, maybe the user intended to ask about the slopes or intercepts. Wait, perhaps the true statement is about the rate (slope) or the initial fill (y-intercept). For example, the steeper line has a higher slope, meaning a faster filling rate. The y-intercept of the steeper line is 50, so at time 0 (x=0), that truck is 50% full, while the other is less. The lines intersect at some x (maybe x=-2), meaning at that time, both trucks are equally full.

But since the options are not provided, I think there's a missing part. Wait, maybe the original problem had options like:

A. The truck represented by the steeper line fills faster.

B. The truck with y-intercept 50 starts empty.

C. The trucks never have the same percentage filled.

D. The truck with lower y-intercept fills faster.

Assuming such options, let's analyze:

Slope = (change in y)/(change in x). The steeper line has a larger slope (since it rises more per unit x), so it fills faster. The y-intercept of the steeper line is 50, so at x=0, it's 50% full. The lines intersect, so at that x, they have the same percentage. So the true statement would be A.

Step2: Confirm with slope calculation

Let's take two points on the steeper line: (0, 50) and (2, let's see, at x=2, y would be 50 + m*2. If the slope is, say, 25 (since from x=0 to x=2, y goes from 50 to 100? Wait, no, the y-axis goes from -100 to 100, with ticks of 10? Wait, the y-axis has 100 at the top, then 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, ..., -100. So each grid square is 10 units? Wait, no, the y-axis: the first tick above 0 is 10? No, the label is y 100 at the top, so maybe each major tick is 20? Wait, no, the problem says y represents percentage filled. So 100% is full. So the y-axis: 100, then maybe 80, 60, 50? Wait, the steeper line passes through (0, 50) and (2, 90)? No, maybe my initial analysis is off.

Alternatively, since the problem is about linear systems (graphs of two lines), the key is to analyze their slopes (rates) and y-intercepts (initial fill). The steeper line has a greater slope, so a faster filling rate. The y-intercept of the steeper line is 50, so at time 0, that truck is 50% full. The lines intersect, so at their intersection point, both trucks have…

Answer:

(Assuming the options include a statement about the steeper line having a faster rate or the y-intercept meaning initial fill. Since the options are missing, but if we assume the true statement is about the slope (rate) or intercept, for example, "The truck with the steeper line has a faster filling rate" or "At x=0, one truck is 50% full", etc. But since the options are not provided, I think there's a mistake. However, if we proceed with the discipline: Mathematics (Algebra), and the solution involves analyzing linear graphs (systems of linear equations), the true statement would relate to slope (rate) or y-intercept (initial condition).)

Wait, the user's question might be incomplete. But based on the graph, the two lines are linear, so the subfield is Algebra (Mathematics). The true statement (if options were about slope, intercept, or intersection) would be about the rate (slope) or initial fill (y-intercept). For example, the steeper line has a higher slope (faster rate), the y-intercept of the steeper line is 50 (so at time 0, that truck is 50% full), and they intersect at some x (so at that time, both are equally full).