To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using the two points given: (4, 2) and (2, 3).
The slope formula is:
m = (y2 – y1) / (x2 – x1)
Plugging in our points:
m = (3 – 2) / (2 – 4) = 1 / -2 = -1/2
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let’s use the point (4, 2).
Using the slope-intercept form:
y = mx + b
We can substitute in the slope and the coordinates of the point:
2 = (-1/2)(4) + b
2 = -2 + b
Now, we solve for b:
b = 2 + 2 = 4
Now we have both the slope and the y-intercept. We can write the equation of the line:
y = -1/2x + 4
So, the equation of the line in slope-intercept form that passes through the points (4, 2) and (2, 3) is:
y = -1/2x + 4