To find the equation of the line that passes through the points (2, 3) and (4, 6), we can use the slope-intercept form of a line, which is given by the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, let’s calculate the slope m using the coordinates of the two points:
m = (y2 – y1) / (x2 – x1)
Substituting the values from our points (2, 3) and (4, 6):
m = (6 – 3) / (4 – 2) = 3 / 2 = 1.5
Now that we have the slope, we can use one of the points to find the y-intercept b. We can use the point (2, 3):
3 = (1.5 * 2) + b
Simplifying this gives:
3 = 3 + b
This leads to:
b = 3 – 3 = 0
Now we have both m and b. We can write the equation of the line:
y = 1.5x + 0
or simply:
y = 1.5x
Thus, the equation of the line passing through the points (2, 3) and (4, 6) is y = 1.5x.