To find the line containing the points (0, 4) and (3, 2), we first need to determine the slope of the line using the formula:
Slope (m) = (y2 – y1) / (x2 – x1)
Here, the two points are (x1, y1) = (0, 4) and (x2, y2) = (3, 2).
Substituting these values into the slope formula gives us:
m = (2 – 4) / (3 – 0) = -2 / 3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y – y1 = m(x – x1)
Using the point (0, 4), we substitute m and the coordinates of the point:
y – 4 = -2/3(x – 0)
Rearranging gives us:
y – 4 = -2/3x
y = -2/3x + 4
This equation y = -2/3x + 4 represents the line that passes through the points (0, 4) and (3, 2).