A line passes through the points (9,8) and (4,9). What is its equation in point-slope form?

1 answer

To find the equation of the line in point-slope form, we first need to calculate the slope of the line that passes through the points \((9,8)\) and \((4,9)\).

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in our points \((x_1, y_1) = (9, 8)\) and \((x_2, y_2) = (4, 9)\):

\[ m = \frac{9 - 8}{4 - 9} = \frac{1}{-5} = -\frac{1}{5} \]

Now that we have the slope \(m = -\frac{1}{5}\), we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

We can choose either of the two points. Let's choose \((9, 8)\):

\[ y - 8 = -\frac{1}{5}(x - 9) \]

Thus, the equation of the line in point-slope form is:

\[ y - 8 = -\frac{1}{5}(x - 9) \]

This is the required equation in point-slope form.