Solve Ratio Problems with Proportions Quick Check 1 of 5 1 of 5 Items Question In which of the following graphs do you recognize a proportional relationship?(1 point) Responses Image with alt text: An illustration shows a coordinate plane with the horizontal axis and vertical axis labeled x and y, but the unit increments are not marked. The origin is marked as 0. A curve is plotted on the graph. The unmarked coordinates of the curve are left parenthesis 0 comma 10 right parenthesis, left parenthesis 5 comma 4 right parenthesis, and left parenthesis 10 comma 4 right parenthesis. A downward diagonal line joins the first two points, then moves rightward as a horizontal line with an arrow at the end. Image with alt text: An illustration shows a coordinate plane with the horizontal axis and vertical axis labeled x and y, but the unit increments are not marked. The origin is marked as 0. An inverted V-shaped curve with an arrow at the end is plotted on the graph. The unmarked coordinates of the inverted V-shaped curve are left parenthesis 0 comma 3 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 10 comma 4 right parenthesis. Image with alt text: An illustration shows a coordinate plane with the horizontal axis and vertical axis labeled x and y, but the unit increments are not marked. The origin is marked as 0. Four points are plotted on the graph. The unmarked coordinates of the plotted points are left parenthesis 2 comma 1 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. A solid arrow begins at the origin and passes through the four points and beyond. Image with alt text: An illustration shows a coordinate plane with the horizontal axis and vertical axis labeled x and y, but the unit increments are not marked. The origin is marked as 0. An upward diagonal line is plotted on the graph. The unmarked coordinates of the upward line are left parenthesis 0 comma 3 right parenthesis, and left parenthesis 8 comma 10 right parenthesis. The line has an arrow at the end
The correct answer is the graph with the solid arrow beginning at the origin and passing through the four plotted points and beyond. This indicates a proportional relationship between the x and y values.
Based on the given descriptions, the graph that represents a proportional relationship is the one with an upward diagonal line plotted on the graph. The unmarked coordinates of the upward line are (0, 3) and (8, 10), and it has an arrow at the end.
To identify a proportional relationship in a graph, you need to look for a straight line passing through the origin (0,0). Proportional relationships are represented by linear graphs that pass through the origin.
Let's analyze each of the given graphs:
1. The first graph has a curve plotted on it and a horizontal line. It does not pass through the origin, so it does not represent a proportional relationship.
2. The second graph has an inverted V-shaped curve. Similar to the first graph, it does not pass through the origin, so it does not represent a proportional relationship.
3. The third graph has four points plotted on it, and a solid arrow passes through these points. The line directly passes through the origin and continues beyond the plotted points. This graph represents a proportional relationship because the line passes through the origin.
4. The fourth graph has an upward diagonal line. It starts at a point (0,3) and ends at a point (8,10). Although it is a straight line, it does not pass through the origin, so it does not represent a proportional relationship.
Therefore, the graph that represents a proportional relationship is the third graph, where a solid arrow passes through four plotted points, including the origin.