To determine the equation of the line in the form y = mx + b that passes through the points (5, 10) and (9, 20), we need to find the values of the slope (m) and the y-intercept (b).
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (5, 10) and (9, 20), we have:
m = (20 - 10) / (9 - 5) = 10 / 4 = 2.5
Now that we have the slope (m = 2.5), we can substitute it into the equation y = mx + b and use one of the given points to solve for the y-intercept (b).
Let's use the point (5, 10):
10 = 2.5(5) + b
10 = 12.5 + b
b = 10 - 12.5
b = -2.5
Therefore, the equation of the line that passes through the points (5, 10) and (9, 20) is:
y = 2.5x - 2.5