A line passes through the points (4, 1) and (2, 9). Which of the following represent the equation in point-slope form?

Question

Select two that apply.

Answer 1

To find the equation of a line in point-slope form, we can use the formula:
\(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope of the line.

First, let's find the slope of the line using the formula:
\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

Using the points (4, 1) and (2, 9), we can calculate the slope:
\(m = \frac{{9 - 1}}{{2 - 4}} = \frac{{8}}{{-2}} = -4\).

Now that we have the slope, we can choose two options that represent the equation in point-slope form:

1. Option 1: \(y - 1 = -4(x - 4)\)
This equation represents the line passing through the point (4, 1) with a slope of -4.

2. Option 4: \(y - 9 = -4(x - 2)\)
This equation represents the line passing through the point (2, 9) with a slope of -4.

Therefore, the correct options are 1 and 4.