Answer:
To find the equation of the line passing through the given pair of points (0, -4) and (5, -4), we can use the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.
To determine the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates of the two points into this formula:
m = (-4 - (-4)) / (5 - 0)
m = 0 / 5
m = 0
Since the slope (m) is zero, this means that the line is horizontal. A horizontal line has a constant y-value regardless of the x-value.
Now, let's find the value of b using one of the given points. We can choose either point (0, -4) or (5, -4). Let's use (0, -4):
y = mx + b
-4 = 0 * 0 + b
-4 = b
Therefore, b is equal to -4.
Now that we have both m and b, we can write the equation of the line:
y = 0x - 4
y = -4
The equation of the line passing through the points (0, -4) and (5, -4) is y = -4.
Explanation: