Question

Write the point-slope form of the equation of the line through the given points:

Through: (4,-4) and (-2,4)
Through (-2,-4) and (0,-4)

Answer 1

To find the point-slope form of the equation, calculate the slope using the given points and apply it in the formula y - y1 = m(x - x1) and we get the equations y + 4 = 0 ,y + 4 = (-4/3)(x - 4).

Step-by-step explanation:

To find the point-slope form of the equation of a line passing through two given points, we first calculate the slope of the line using the formula:

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

Then, we can choose either of the given points and plug its coordinates and the slope into the point-slope form equation:

y - y1 = m(x - x1)

Let's apply this method to the two sets of given points:

1. Through: (4,-4) and (-2,4)
   Slope = (4 - (-4)) / (-2 - 4) = 8 / -6 = -4/3
   Using point (4, -4):
   y - (-4) = (-4/3)(x - 4)
   y + 4 = (-4/3)(x - 4)
2. Through: (-2,-4) and (0,-4)
   Slope = (-4 - (-4)) / (0 - (-2)) = 0 / 2 = 0
   Using point (-2, -4):
   y - (-4) = 0(x - (-2))
   y + 4 = 0