Question

Write the equation of the line that goes through the points: (2, 6) and (-2, 14).

y = 2x + 2
y = -2x + 10
y = -1/2x + 7
y = 1/2x + 5

Answer 1

The equation of the line passing through the points (2, 6) and (-2, 14) is y = -2x + 10, found by calculating the slope and applying it to the point-slope form of a linear equation.

Step-by-step explanation:

To write the equation of the line that passes through the points (2, 6) and (-2, 14), we first need to find the slope (m) of the line using the formula:

m = (Y2 - Y1) / (X2 - X1)

Using the given points:

m = (14 - 6) / (-2 - 2) = 8 / (-4) = -2

Now that we have the slope, we can use the point-slope form to find the equation of the line. The point-slope form is:

y - y1 = m(x - x1)

Using one of the given points (2, 6) and the slope m = -2:

y - 6 = -2(x - 2)

This simplifies to:

y - 6 = -2x + 4

y = -2x + 10

Therefore, the equation of the line is y = -2x + 10.