Final answer:
To find two points on the graph of a line given two other points, we need to first determine the equation of the line using the slope formula. Then, we can choose any two values of x and find the corresponding y-values using the equation. In this case, the two points that lie on the graph of the line are (0, 16) and (5, 1).
Step-by-step explanation:
To find two points that lie on the graph of the line, we need to identify the equation of the line. We can do this by finding the slope of the line using the two given points. Let's call the two given points (x1, y1) and (x2, y2).
The slope of the line is given by the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values of the given points, we have m = (7 - 10) / (3 - 2) = -3.
Now that we have the slope, we can use the point-slope form of the equation, y - y1 = m(x - x1). Plugging in the values of one of the given points, we have y - 10 = -3(x - 2). Simplifying the equation, we get y = -3x + 16.
We can then choose any two values of x and plug them into the equation to find the corresponding y-values. Let's choose x = 0 and x = 5:
For x = 0, y = -3(0) + 16 = 16. Therefore, the point (0, 16) lies on the graph of the line.
For x = 5, y = -3(5) + 16 = 1. Therefore, the point (5, 1) lies on the graph of the line.