Answer:
The equation of the line that passes through the points (3,4) and (-1,-4) is y = 2x + 2.
Explanation:
The equation of the line that passes through the points (3,4) and (-1,-4) can be found using the point-slope form of a line:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, m is the slope of the line, and (x,y) are the coordinates of any other point on the line.
First, we'll find the slope of the line using the two points:
m = (y2 - y1) / (x2 - x1) = (-4 - 4) / (-1 - 3) = -8 / -4 = 2
Next, we'll use one of the points and the slope to write the equation in the point-slope form:
y - 4 = 2(x - 3)
Expanding the right side:
y - 4 = 2x - 6
Adding 4 to both sides:
y = 2x + 2
So the equation of the line that passes through the points (3,4) and (-1,-4) is y = 2x + 2.