To find the equation of the line that passes through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is one of the points on the line.
First, let's find the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (2 - (-4)) / (1 - 5)
m = 6 / (-4)
m = -3/2
Now, we can use either of the two given points to write the equation of the line. Let's use (5, -4):
y - (-4) = (-3/2)(x - 5)
Simplifying, we get:
y + 4 = (-3/2)x + 15/2
Subtracting 4 from both sides, we get:
ANSWER- y = (-3/2)x + 7/2