How do you write the equation in slope-intercept form for a line that passes through the points (3, 1) and (2, 5)?

To write the equation of a line in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b) of the line passing through the given points (3, 1) and (2, 5).

Step 1: Calculate the slope (m).

The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

In our case, let (x₁, y₁) = (3, 1) and (x₂, y₂) = (2, 5).

So, we can plug in these coordinates:

m = (5 – 1) / (2 – 3) = 4 / -1 = -4

Step 2: Use slope and one point to find y-intercept (b).

We can now use the slope and one of the points to find the y-intercept (b). Let’s use the point (3, 1). We substitute the slope (m) and the coordinates of the point into the slope-intercept form:

y = mx + b

1 = -4(3) + b

1 = -12 + b

Now, solve for b:

b = 1 + 12 = 13

Step 3: Write the equation in slope-intercept form.

Now that we have both m and b, we can write the equation:

y = -4x + 13

This is the equation of the line in slope-intercept form that goes through the points (3, 1) and (2, 5).