To find the equation in point-slope form of the line that passes through the points (3, 4) and (0, 2), we first need to determine the slope of the line.
The formula for the slope (
m) between two points
(x_1, y_1) and
(x_2, y_2) is:
m = (y_2 – y_1) / (x_2 – x_1)
Using our points, let’s assign:
- x_1 = 3, y_1 = 4
- x_2 = 0, y_2 = 2
Now we can substitute these values into our slope formula:
m = (2 – 4) / (0 – 3) = -2 / -3 = 2/3
Now that we have our slope, we can use one of the points to write the equation in point-slope form. The point-slope form of a line’s equation is expressed as:
y – y_1 = m(x – x_1)
Substituting our slope
(m = 2/3)
and using the point (3, 4):
y – 4 = (2/3)(x – 3)
Thus, the equation of the line in point-slope form is:
y – 4 = (2/3)(x – 3)
You can also use the point (0, 2) to create the same equation:
y – 2 = (2/3)(x – 0)
Both forms accurately represent the line passing through points (3, 4) and (0, 2). This point-slope form is particularly useful for quickly identifying the slope and a point on the line.