Final answer:
Without additional information about the line's equation or slope, it's impossible to determine two other points on the same line as (0,1) using the given table of points.
Step-by-step explanation:
If we have the point (0,1) on a line, and we need to name two other points on this line, we would need more information to determine the exact line and the other points on it. However, since no additional information about the line's equation or slope is given, we cannot use the provided table of points to confidently determine two additional points on the same line as (0,1). Generally, to find other points on the line, we could use the line's equation or calculate the slope, using the formula (Y₂-Y₁)/(X₂-X₁), if we know at least two points on the line. This would allow us to find additional points by applying this dependence of y on x. The points in the table provided, such as (1,5), (2,10), (3,7), and (4,14), may or may not lie on the same line as (0,1) without more data.
If the point (0,1) is on the line, we can find two other points on the line by using the concept of slope. The slope of a line is the change in y divided by the change in x between any two points. Let's pick two other points: (1,5) and (2,10) from the given table. To find the slope, we can use the formula: slope = (Y2 - Y1) / (X2 - X1). Substituting the values, we have slope = (10 - 5) / (2 - 1) = 5 / 1 = 5. Now, we can use either of the two points and the slope to find the equation of the line. Let's use the point (1,5).Using the point-slope form of the equation for a line, y - y1 = m(x - x1), where m is the slope, x1 and y1 are the coordinates of a point on the line, we can substitute the values into the equation. y - 5 = 5(x - 1). Simplifying, we get y - 5 = 5x - 5. Rearranging the equation, we get y = 5x. Therefore, two other points on the line are (1,5) and (2,10).