The amount of money earned for hours spent babysitting is displayed on the gragh. Derive the equation of the line through the origin. There is money and and hours worked the is 16.50 22 5.50 and 11 and the hours are 1 2 3 4 5 and 6
To derive the equation of the line through the origin, we first need to find the slope of the line. The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. In this case, we can use the points (1, 5.50) and (6, 16.50) to calculate the slope:
m = (16.50 - 5.50) / (6 - 1)
m = 11 / 5
m = 2.20
Now that we have the slope of the line, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is any point on the line. Since the line passes through the origin (0, 0), we can use this point in the equation:
y - 0 = 2.20(x - 0)
Simplifying, we get:
y = 2.20x
Therefore, the equation of the line through the origin is y = 2.20x.