To find the equation of the line that contains the points (0, 4) and (3, 2), 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.
Step 1: Calculate the slope
The slope m of a line through two points, (x1, y1) and (x2, y2), can be calculated using the formula:
m = (y2 – y1) / (x2 – x1)
For our points, we have:
- (x1, y1) = (0, 4)
- (x2, y2) = (3, 2)
Substituting in the values:
m = (2 – 4) / (3 – 0) = -2 / 3
Step 2: Find the y-intercept
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, 4), where x = 0, to find b.
Using the equation of the line:
y = mx + b
Substituting the known values (x = 0, y = 4, m = -2/3):
4 = (-2/3)(0) + b
This simplifies to:
b = 4
Step 3: Write the equation of the line
Now that we have both the slope and the y-intercept, we can write the equation of the line:
y = -2/3x + 4
In conclusion, the equation of the line that contains the points (0, 4) and (3, 2) is:
y = -2/3x + 4