Given the following equation of a graph:
For us to be able to determine which points lie on the graph, we will be plugging in each given coordinate to see if it will make the equation valid.
a.) x, y = 6, 15
y = 2x + 3
15 = 2(6) + 3
15 = 12 + 3
15 = 15 (The equation is valid)
Therefore, (6, 15) lies on the graph.
b.) x, y = 2, 2
y = 2x + 3
2 = 2(2) + 3
2 = 4 + 3
2 = 7 (The equation is invalid)
Therefore, (2,2) doesn't lie on the graph.
c.) x, y = -1, 1
y = 2x + 3
1 = 2(-1) + 3
1 = -2 + 3
1 = 1 (The equation is valid)
Therefore, (-1, 1) lies on the graph.
d.) x, y = -6, -10
y = 2x + 3
-10 = 2(-6) + 3
-10 = -12 + 3
-10 = -9 (The equation is invalid)
Therefore, (-6, -1) doesn't lie on the graph.
In summary, the points that lie on the graph are (6, 15) and (-1, 1).