To find the equation of the line in slope-intercept form (which is y = mx + b, where m is the slope and b is the y-intercept), we first need to determine the slope (m) of the line that passes through the two given points: (3, 1) and (1, 5).
The formula to calculate the slope m between two points (x_1, y_1) and (x_2, y_2) is:
m = (y_2 – y_1) / (x_2 – x_1)
Here, we can assign: (x_1, y_1) = (3, 1) and (x_2, y_2) = (1, 5).
Now plug in the values:
m = (5 – 1) / (1 – 3) = 4 / -2 = -2
So, the slope m is -2.
Next, we need to find the y-intercept b. We can use the slope-intercept form of the equation and one of the points to solve for b. Let’s use the point (3, 1).
Substituting the values into the slope-intercept equation:
1 = -2(3) + b
This simplifies to:
1 = -6 + b
Now, solve for b:
b = 1 + 6 = 7
Now that we have both the slope (-2) and the y-intercept (7), we can write the equation of the line:
y = -2x + 7
In conclusion, the equation of the line in slope-intercept form that passes through the points (3, 1) and (1, 5) is:
y = -2x + 7