(4, 0), (3, −1), (6, 3), (2, −4)
To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation, given by y = mx + b, where m is the slope and b is the y-intercept.
Let's find the slope (m) of the line passing through the points (4, 0) and (3, -1):
m = (y2 - y1) / (x2 - x1)
m = (-1 - 0) / (3 - 4)
m = -1 / -1
m = 1
Now, let's choose one of the points, (3, -1), and plug in the values of x, y, and m into the slope-intercept form to find the y-intercept (b):
-1 = 1(3) + b
-1 = 3 + b
b = -1 - 3
b = -4
The equation of the line passing through the points (4, 0) and (3, -1) is y = x - 4.
Let's now find the equation of the line passing through the points (6, 3) and (2, -4):
m = (-4 - 3) / (2 - 6)
m = -7 / -4
m = 7/4
Using the point (6, 3) and the slope, we find:
3 = (7/4)(6) + b
3 = 42/4 + b
3 = 21/2 + b
b = 3 - 21/2
b = 6/2 - 21/2
b = -15/2
Therefore, the equation of the line passing through the points (6, 3) and (2, -4) is y = (7/4)x - 15/2.