To find the equation of the line that passes through the points (0, 2) and (4, 6), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to calculate the slope (m) of the line. The formula for the slope between two points 0(x1, y1) and (x2, y2) is given by:
m = (y2 – y1) / (x2 – x1)
Substituting our points (0, 2) and (4, 6):
m = (6 – 2) / (4 – 0) = 4 / 4 = 1
Now that we have the slope, we can use one of the points to find the y-intercept (b). We’ll use the point (0, 2), which is the y-intercept. So:
b = 2
Now we have the slope (m = 1) and the y-intercept (b = 2). Plugging these values into the slope-intercept form gives:
y = 1x + 2
Or more simply:
y = x + 2
This is the equation of line CD that passes through the points (0, 2) and (4, 6).