Final Answer:
The y-value for x = 25 is approximately 49.
Step-by-step explanation:
A line of best fit was drawn to the plotted points in the given data set. The line of best fit is a representation of the trend seen in the data set. The line of best fit is also known as a linear regression line. It is a straight line that is used to approximate the data points in the data set as closely as possible.
The line of best fit can be determined using the equation of a straight line: y = mx + c, where m is the slope of the line and c is the y-intercept. To determine the value of y for x = 25, we need to find the equation of the line of best fit. To do this, we need to calculate the slope (m) of the line.
The slope of the line of best fit can be calculated by using the formula m = (y2-y1)/(x2-x1). To calculate the slope, we need to choose two points on the line of best fit and find their coordinates. For our data set, the points (0,2) and (50,100) can be used. Using these points, we can calculate the slope of the line of best fit as m = (100-2)/(50-0) = 2.
Once the slope (m) is known, we can use the equation of a straight line to find the equation of the line of best fit. The equation of the line of best fit is y = 2x + c. To find the y-value for x = 25, we can substitute the values into the equation. This gives us y = 2(25) + c.
We can calculate the value of c by substituting the coordinates of one of the points on the line of best fit into the equation. For our data set, we can use the coordinates of the point (0,2). Substituting these values into the equation gives us 2 = 2(0) + c, which simplifies to c = 2.
Substituting the value of c into the equation of the line of best fit gives us y = 2x + 2. Substituting x = 25 into this equation gives us y = 2(25) + 2 = 52.
Therefore, the y-value for x = 25 is approximately 49.