Find an equation of the line containing the given pair of points.
(4,1) and (12,8)
The slope of the line passing through the points (4,1) and (12,8) can be found using the formula:
m = (y2 - y1)/(x2 - x1)
Let's substitute the given values:
m = (8 - 1)/(12 - 4)
m = 7/8
The slope of the line is 7/8. Next, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Let's choose one of the points, such as (4,1), and substitute the values:
y - 1 = (7/8)(x - 4)
Multiplying both sides by 8 to eliminate the fraction:
8y - 8 = 7(x - 4)
Expanding the right side:
8y - 8 = 7x - 28
Moving the terms to the other side:
7x - 8y = 20
Therefore, the equation of the line passing through the points (4,1) and (12,8) is 7x - 8y = 20.