Question

Write the equation of the linear function that passes through the points (2,1) and (5,10). 

y = ___ x +____

Answer 1

To find the equation of the linear function passing through the points (2,1) and (5,10), we first need to find the slope (m) and then use the point-slope form of the equation of a line.

First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (10 - 1) / (5 - 2)
m = 9 / 3
m = 3

Now that we have the slope, we can use the point-slope form of the equation of a line with one of the points:
y - y1 = m(x - x1)
Using the point (2,1):
y - 1 = 3(x - 2)
y - 1 = 3x - 6
y = 3x - 6 + 1
y = 3x - 5

Therefore, the equation of the linear function passing through the points (2,1) and (5,10) is y = 3x - 5.