Final answer:
To find the equation of the line passing through (3,4) and (4,6), we calculate the slope as 2 and then use the point-slope form to find the equation, which is y = 2x - 2.
Step-by-step explanation:
To find the equation of a line containing the points (3,4) and (4,6), first we calculate the slope (m) of the line using the formula:
m = (y2-y1)/(x2-x1)
Substituting the given points:
m = (6-4)/(4-3) = 2/1 = 2
Now that we have the slope, we use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Let's use point (3,4):
y - 4 = 2(x - 3)
Simplifying, we get the equation in slope-intercept form (y = mx + b):
y - 4 = 2x - 6
y = 2x - 2
Thus, the equation of the line is y = 2x - 2.