To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) of the line that passes through the two given points.
The two points are (3, 1) and (1, 5). We can calculate the slope using the formula:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (3, 1) and (x2, y2) = (1, 5).
Plugging in the values, we get:
m = (5 – 1) / (1 – 3) = 4 / -2 = -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 (3, 1).
We can plug in the values into the slope-intercept equation:
y = mx + b
Selecting point (3, 1):
1 = -2(3) + b
Now we simplify:
1 = -6 + b
Adding 6 to both sides gives:
b = 7
Now we have both the slope and the y-intercept. Thus, the equation of the line in slope-intercept form is:
y = -2x + 7