Question

Write the equation of the line passing through the points (−1, 2) and (3, 4)
Responses
A y = 2x − 2y = 2x − 2
B y = 2x − 10y = 2x − 10
C y = 1/2 x + 5/2
D y = 1/2 x − 5/2

Answer 1

To find the equation of the line passing through two points, we can use the equation:

y - y1 = (x - x1)(y2-y1)/(x2-x1)

In this case, our points are (-1, 2) and (3, 4).

Using the equation, we can substitute the coordinates into the equation to find the equation of the line.

For the first point, (-1, 2):

y - 2 = (x - (-1))(4 - 2)/(3 - (-1))
y - 2 = (x + 1)(2)/(4)
y - 2 = (2x + 2)/4
y - 2 = (1/2)x + 1/2

For the second point, (3, 4):
y - 4 = (x - 3)(4 - 2)/(3 - 3)
y - 4 = (x - 3)(2)/(0)
There is an undefined slope since the denominator is equal to 0. Therefore, we can't use this point to find the equation of the line.

Therefore, the equation of the line passing through the points (-1, 2) and (3, 4) is:

y - 2 = (1/2)x + 1/2 (option C)