To find the equation of the line that passes through the points (3, 4) and (2, 1), we first need to determine the slope (m) of the line. The slope can be calculated using the formula:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (3, 4) and (x2, y2) = (2, 1).
Plugging in the values:
m = (1 – 4) / (2 – 3) = (-3) / (-1) = 3
So, the slope of the line is 3.
Next, we use the slope-intercept form of the line, which is represented as:
y = mx + b
We already have the slope (m = 3). To find the y-intercept (b), we can substitute one of the points into the equation. We’ll use the point (3, 4):
4 = 3(3) + b
4 = 9 + b
Now, solving for b:
b = 4 – 9 = -5
Now that we have both the slope and the y-intercept, we can write the equation of the line:
y = 3x – 5
This is the equation of the line in slope-intercept form that passes through the points (3, 4) and (2, 1).