To find the equation of the line in point-slope form that passes through the points (0, 6) and (1, 3), we first need to calculate the slope of the line.
The slope (m) is calculated using the formula:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (0, 6) and (x2, y2) = (1, 3). Substituting these values in, we get:
m = (3 – 6) / (1 – 0) = -3 / 1 = -3
Now that we have the slope, we can use the point-slope form of a line, which is:
y – y1 = m(x – x1)
We can use either of the two points for (x1, y1). Let’s choose (0, 6):
y – 6 = -3(x – 0)
This simplifies to:
y – 6 = -3x
Finally, we can rearrange it to the standard form:
y = -3x + 6
Thus, the equation in point-slope form is:
y – 6 = -3(x – 0)