Three points are on a coordinate plane: A(1, 5), B(-2, -4), and C(6, -4).

1.
Write an equation in point-slope form of the line with slope -1 that contains point C.
2.
Write an equation in point-slope form of the line that contains points A an B.
3.
Write an equation of the line that contains B and C.

1. C(6,-4), m = -1. (X,Y).

m = y-(-4)/(X-6) = -1,

Eq: Y+4 = -1(X-6).

2. A(1,5), B(-2,-4),
m = (-4-5)/(-2-2) = -9/-4 = 9/4.

A(1,5), X,Y),
m = (Y-5/(X-1) = (9/4)/1,
Cross multiply:

Eq: Y-5 = 9/4(X-1).

3. Similar to 1 and 2.

1. To write an equation in point-slope form of the line with slope -1 that contains point C, we need to use the point-slope form equation y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point and m is the slope of the line. In this case, the coordinates of point C are (6, -4), and the slope is -1.

Using the point-slope form equation, we have y - (-4) = -1(x - 6). Simplifying this equation, we get y + 4 = -x + 6.

The equation in point-slope form that satisfies these conditions is y + 4 = -x + 6.

2. To write an equation in point-slope form of the line that contains points A and B, we need to find the slope first. The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.

The coordinates of point A are (1, 5) and the coordinates of point B are (-2, -4). Plugging in these values, we get m = (-4 - 5) / (-2 - 1) = -9 / -3 = 3.

Now that we have the slope (m = 3), we can use the point-slope form equation. Let's choose point A as (x1, y1). The equation becomes y - 5 = 3(x - 1).

The equation in point-slope form that contains points A and B is y - 5 = 3(x - 1).

3. To write an equation of the line that contains points B and C, we can follow a similar approach to the previous example.

The coordinates of point B are (-2, -4) and the coordinates of point C are (6, -4). We can find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).

Plugging in these values, we get m = (-4 - (-4)) / (6 - (-2)) = 0 / 8 = 0.

Since the slope is 0, we have a horizontal line. In this case, the y-coordinate remains constant throughout. From points B and C, we can see that the constant y-coordinate is -4.

Thus, the equation of the line that contains points B and C is y = -4.