Write the equation of the linear function that passes through the points ( 1, 1) and ( 3 , 5 ) .
To find the equation of the linear function that passes through the given points, we first need to find the slope of the line.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given points (1, 1) and (3, 5):
m = (5 - 1) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using point (1, 1):
y - 1 = 2(x - 1)
y - 1 = 2x - 2
y = 2x - 1
Therefore, the equation of the linear function that passes through the points (1, 1) and (3, 5) is y = 2x - 1.