Final answer:
The equation of the line that passes through the points (3,6) and (4,10) using function notation is y = 4x - 6.
Step-by-step explanation:
The equation of the line that passes through the points (3,6) and (4,10) using function notation can be found using the slope-intercept form of the equation:
y = mx + b
where m is the slope and b is the y-intercept.
First, we need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula:
m = (10 - 6) / (4 - 3) = 4 / 1 = 4
Now that we have the slope, we can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b).
Using the point (4,10):
10 = 4(4) + b
Simplifying the equation:
10 = 16 + b
b = 10 - 16 = -6
Therefore, the equation of the line is:
y = 4x - 6