How do you find the equation in point-slope form of the line that goes through the points (0, 6) and (1, 3)?

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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 determine the slope of the line. The slope (m) can be calculated using the slope formula:

m = (y2 - y1) / (x2 - x1)

Here, we can assign:

  • (x1, y1) = (0, 6)
  • (x2, y2) = (1, 3)

Now substituting the values into the formula:

m = (3 - 6) / (1 - 0) = -3 / 1 = -3

The slope of the line is -3. Next, we can use the point-slope formula, which is:

y - y1 = m(x - x1)

Using the point (0, 6) (where x1 = 0 and y1 = 6), we substitute m and the coordinates:

y - 6 = -3(x - 0)

This simplifies to:

y - 6 = -3x
y = -3x + 6

Thus, the equation of the line in point-slope form passing through the points (0, 6) and (1, 3) is:

y - 6 = -3(x - 0)

This format allows you to see both the slope of the line and the specific point it passes through. If you need it in slope-intercept form, it’s y = -3x + 6!

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