Answer:
The equation of the line is y = 2.5x - 4.
Explanation:
To find the equation of a line, we can use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope, we can use the formula:
m = (change in y) / (change in x)
Let's calculate the slope using the given points (2, 1) and (4, 6):
(change in y) = 6 - 1 = 5
(change in x) = 4 - 2 = 2
m = 5 / 2 = 2.5
Now that we have the slope, we can use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
Using the point (2, 1) and the slope m = 2.5, we have:
y - 1 = 2.5(x - 2)
Now, let's simplify the equation:
y - 1 = 2.5x - 5
y = 2.5x - 4
Therefore, the equation of the line is y = 2.5x - 4.