To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (6, 1) and (3, 2), we will follow these steps:
Step 1: Calculate the slope (m)
The slope (m) of a line can be found using the formula:
m = (y2 – y1) / (x2 – x1)
Here, we can label the points as follows:
- (x1, y1) = (6, 1)
- (x2, y2) = (3, 2)
Substituting the values into the slope formula:
m = (2 – 1) / (3 – 6) = 1 / -3 = -1/3
Step 2: Use the slope to find the y-intercept (b)
To find the y-intercept (b), we can use the slope-intercept form of the equation and substitute one of the points. We know:
y = mx + b
Using the point (6, 1):
- 1 = (-1/3)(6) + b
This simplifies to:
1 = -2 + b
To solve for b, add 2 to both sides:
b = 1 + 2 = 3
Step 3: Write the equation of the line
Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the line:
y = -1/3x + 3
Conclusion
The equation of the line in slope-intercept form that passes through the points (6, 1) and (3, 2) is:
y = -1/3x + 3
This equation tells us that for every increase of 1 in x, y decreases by 1/3, and the line crosses the y-axis at the point (0, 3).