Question

Write an equation of the line through the given points (6, -4) and (-1, 2).

a) The question is incomplete.
b) y = -2x + 8
c) y = 2x - 8
d) y = -2x - 8

Answer 1

The equation of the line passing through the points (6, -4) and (-1, 2) is calculated to be y = -6/7x + 8/7, by determining the slope and applying the point-slope form.

Step-by-step explanation:

To find the equation of a line that passes through two points, (6, -4) and (-1, 2), we first calculate the slope (m) using the formula:

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

By plugging in the coordinates:

m = (2 - (-4)) / (-1 - 6)

m = (2 + 4) / (-7)

m = 6 / -7

m = -6/7

Now that we have the slope, we can use the point-slope form, y - y1 = m(x - x1), and one of the points to find the equation. Let's use the point (6, -4):

y - (-4) = -6/7(x - 6)

y + 4 = -6/7x + 6(6/7)

y + 4 = -6/7x + 36/7

y = -6/7x + 36/7 - 4

y = -6/7x + 36/7 - 28/7

y = -6/7x + 8/7

So the equation of the line in slope-intercept form is y = -6/7x + 8/7, which is not reflected in any of the answer choices given.