Write the equation of the line that passes through the points left bracket, 2, comma, minus, 8, right bracket(2,−8) and left bracket, minus, 1, comma, 4, right bracket(−1,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

To find the equation of the line that passes through the points (2, -8) and (-1, 4), we can use the point-slope form of the equation, which is given as:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.

First, let's find the slope (m) using the two given points:
m = (y2 - y1) / (x2 - x1)

m = (4 - (-8)) / (-1 - 2)

m = 12 / -3

m = -4

Now, we can choose either of the given points to substitute into the point-slope form. Let's use the point (2, -8):

y - (-8) = -4(x - 2)

Simplifying this equation further:

y + 8 = -4x + 8

y = -4x + 8 - 8

y = -4x

Therefore, the equation of the line passing through the points (2, -8) and (-1, 4) is y = -4x.