To find the equation of the line connecting the points (-4,7) and (2,-2), you can use the point-slope form of a linear equation:
The formula is: y - y1 = m(x - x1)
Where (x1, y1) is one of the points on the line, and m is the slope of the line.
First, calculate the slope (m) using the given points:
m = (y2 - y1) / (x2 - x1)
m = (-2 - 7) / (2 - (-4))
m = (-9) / (2 + 4)
m = -9 / 6
m = -3/2
Now, you can choose either of the two points, let's use (-4, 7):
x1 = -4
y1 = 7
Now, plug these values into the point-slope equation:
y - 7 = (-3/2)(x - (-4))
Simplify further:
y - 7 = (-3/2)(x + 4)
To put it in slope-intercept form (y = mx + b), expand and isolate y:
y - 7 = (-3/2)x - 6
Add 7 to both sides:
y = (-3/2)x + 1
So, the equation of the line connecting the points (-4,7) and (2,-2) is:
y = (-3/2)x + 1