To determine the equation of the line that passes through the points (0, 2) and (60, 0), we can use the two-point form of the equation of a line. The general equation can be represented as:
y - y1 = m(x - x1)
Where:
- (x1, y1) is one of the points the line passes through, and
- m is the slope of the line.
First, we need to calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (0, 2) as (x1, y1) and (60, 0) as (x2, y2):
m = (0 - 2) / (60 - 0) = -2 / 60 = -1/30
Now that we have the slope, we can substitute (x1, y1) and the slope into the equation:
y - 2 = -1/30(x - 0)
To simplify it, we can multiply through by 30 to eliminate the fraction:
30(y - 2) = -1(x)
This results in:
30y - 60 = -x
Rearranging it gives us the standard form:
x + 30y = 60
Thus, the equation of the line that passes through the points (0, 2) and (60, 0) is:
x + 30y = 60
In slope-intercept form (y = mx + b), it can be expressed as:
y = (-1/30)x + 2
In conclusion, the equation of the line in standard form is x + 30y = 60.