To find the equation of the line that passes through the points (2, 2) and (1, 4), we first need to determine the slope of the line.
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:
m = (y2 – y1) / (x2 – x1)
Substituting our given points into this formula, we have:
x1 = 2, y1 = 2, x2 = 1, y2 = 4
Now, substituting these values into the slope formula:
m = (4 – 2) / (1 – 2) = 2 / -1 = -2
The slope of the line is -2. Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
y – y1 = m(x – x1)
Choosing the first point (2, 2), we substitute:
y – 2 = -2(x – 2)
Simplifying this equation:
y – 2 = -2x + 4
y = -2x + 6
Thus, the equation of the line that passes through the points (2, 2) and (1, 4) is:
y = -2x + 6
Alternatively, if you want it in standard form, you can rearrange it:
2x + y = 6
This line has a slope of -2 and a y-intercept of 6, meaning it goes down two units for every one unit it moves to the right, intersecting the y-axis at 6.