What is the equation of the line that passes through the points (−2, 4) and (−4, −2)?

To find the equation of the line that passes through two points, specifically (−2, 4) and (−4, −2), we start by calculating the slope of the line using the formula:

[ m = \frac{y_2 - y_1}{x_2 - x_1}

]

Substituting in the given points, we have:

[ m = \frac{-2 - 4}{-4 - (-2)} = \frac{-6}{-4 + 2} = \frac{-6}{-2} = 3 ]

Now that we have the slope (m = 3), we can use the point-slope form of the equation of a line, which is:

[ y - y_1 = m(x - x_1) ]

We can choose either point; using (−2, 4):

[ y - 4 = 3(x + 2) ]

Distributing the slope:

[ y - 4 = 3x + 6 ]

Now, solve for y:

[ y = 3x + 10 ]

This matches the equation provided in option A. Therefore