Final answer:
To find the values of x and y that make a quadrilateral a parallelogram, we need to consider the properties of parallelograms and solve the given equation to find the corresponding points. By plotting these points on a graph and checking the properties of parallelograms, we can determine if the quadrilateral is a parallelogram.
Step-by-step explanation:
To find the values of x and y that make a quadrilateral a parallelogram, we need to consider the properties of parallelograms. One key property is that opposite sides of a parallelogram are parallel and congruent. Another property is that opposite angles of a parallelogram are congruent.
In this case, the given equation is y = 9 + 3x. To determine the values of x and y that make the quadrilateral a parallelogram, we need to find values of x that satisfy the equation, and then calculate the corresponding values of y. By plugging in different values of x, we can determine multiple points that lie on the line represented by the equation. These points can be used to construct a quadrilateral on a graph. To determine if the quadrilateral is a parallelogram, we can check if opposite sides are parallel and congruent and if opposite angles are congruent.
For instance, if we choose x = 0, then y can be calculated as y = 9 + 3(0) = 9. This gives us the point (0, 9). By choosing other values of x, we can find more points, such as (1, 12) and (2, 15). Using these points, we can plot them on a graph and connect them with lines to form a quadrilateral. Finally, we can check if opposite sides and angles satisfy the properties of a parallelogram to determine if the values of x and y indeed make the quadrilateral a parallelogram.