Question

Determine the equation

C.) through (3,-9) and (-2,-4)

Answer 1

y= -x-6

Explanation:

We can use the point-slope form of a linear equation to determine the equation of the line passing through the two given points:

Point-Slope Form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, let's find the slope of the line passing through (3, -9) and (-2, -4):

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

m = (-4 - (-9)) / (-2 - 3)

m = 5 / (-5)

m = -1

Now we can use one of the given points and the slope we just found to write the equation:

y - (-9) = -1(x - 3)

Simplifying:

y + 9 = -x + 3

Subtracting 9 from both sides:

y = -x - 6

Therefore, the equation of the line passing through (3,-9) and (-2,-4) is y = -x - 6.

Answer 2

y = -x - 6

Explanation:

(3, -9); (-2, -4)

m = (y_2 - y_1)/(x_2 - x_1) = (-4 - (-9))/(-2 - 3) = 5/(-5) = -1

y = mx + b

-9 = -1(3) + b

-9 = -3 + b

b = -6

y = -x - 6