1. Yes, the line graph shows the graph of a linear equation in two variables because it was plotted on an xy coordinate plane.
2. The line graph is located in quadrant I because the x-coordinate and y-coordinate are both positive.
3. Even though the line graph consists of several line segments, the slope of each segment are the same.
4. The graph represents a proportional relationship between the x-variable and y-variable.
In Mathematics and Geometry, a linear equation is a type of function with a constant slope and whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
Part 1.
Based on the definition of a linear equation, we can logically deduce that the line graph represents the graph of a linear equation in two variables because it was plotted on an xy coordinate plane.
Part 2.
This line graph is located in quadrant I (first quadrant) because the x-coordinate and y-coordinate are both positive.
Part 3.
Even though this line graph is composed of several line segments, the slope of each segment are constant and the same;
Slope of segment AB = 1/1.5 = 2/3.
Slope of segment BC = (2 - 1)/(3 - 1.5) = 2/3.
Part 4.
In conclusion, the graph represents a proportional relationship between the x-variable and y-variable because its line passes through the origin (0, 0).