How do you write an equation in slope intercept form for a line with points (3, 1) and (2, 5)?

To write an equation in slope-intercept form, which is expressed as y = mx + b, we first need to determine the slope (m) of the line that passes through the two given points: (3, 1) and (2, 5).

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

m = (y₂ – y₁) / (x₂ – x₁)

Using our points, (x₁, y₁) = (3, 1) and (x₂, y₂) = (2, 5), we can substitute these values into the slope formula:

m = (5 – 1) / (2 – 3) = 4 / -1 = -4

Now that we have the slope, m = -4, we can use one of the points to find the y-intercept (b). We can use the point (3, 1) for this example.

We substitute the x and y values into the slope-intercept equation:

1 = -4(3) + b

This simplifies to:

1 = -12 + b

Now, add 12 to both sides to solve for b:

b = 1 + 12 = 13

Now we have the slope and the y-intercept. We can write the final equation in slope-intercept form:

y = -4x + 13