Question

The points A, B, and C have the coordinates A(-2, 0), B(2, -2), and C(1, 3).

Determine the equations of the following lines in slope-intercept form:

The equation for line AB.
The equation for line BC.
The equation for line CA.

Answer 1

To find the equations of the lines, we need to find the slope and y-intercept. For line AB, the equation is y = -1/2x + 1. For line BC, the equation is y = 5x - 10. And for line CA, the equation is y = -3x - 6.

Step-by-step explanation:

To find the equation of a line in slope-intercept form, we need both the slope (m) and the y-intercept (b).

For line AB, we can use the coordinates A(-2, 0) and B(2, -2) to find the slope:

m = (y2 - y1) / (x2 - x1) = (-2 - 0) / (2 - (-2)) = -2/4 = -1/2

Using the point-slope form, we have: y - y1 = m(x - x1)

Plugging in the values for A(-2, 0): y - 0 = (-1/2)(x - (-2))

Simplifying the equation gives us the equation for line AB: y = -1/2x + 1

Similarly, we can find the equations for lines BC and CA using the given coordinates:

For line BC: y - y1 = m(x - x1)

For line CA: y - y1 = m(x - x1)

Therefore, the equations for line BC and line CA are: y = 5x - 10 and y = -3x - 6, respectively.