Answer:
y = -6
Explanation:
We're looking for a linear equation in the form y=mx+b, where m is the slope and b is the y-intercept. To solve, we need to calculate the slope and then calculate the y-intercept.
1. Slope
Start by calculating the slope, which needs the rise and run:
Rise (how much it goes up): (-6) - (-6) = 0
The first -6 comes from the y position of the first point (1,-6), and the second -6 comes from the y position of the second point (5,-6).
Run (how much it goes to the side): 1 - 5 = -4
The 1 comes from the x position of the first point (1,-6), and the 5 comes from the x position of the second point (5,-6).
The slope is equal to the rise over the run:
Slope = rise ÷ run = 0 ÷ (-4) = 0
Thus, the slope is 0. So far, our equation looks like y=0x+b, which is equivalent to y=b.
2. y-intercept
To find the y-intercept, we take a point and plug it into out equation. We can take either point, and I'm going to take the first point (1,-6). We plug x=1 and y=-6 into our equation and get:
y=0x+b
-6 = 0(1)+b
-6 = 0+b
-b = b
b = -b
Thus, our y-intercept is -6.
3. Putting it all together
When we put the slope and y-intercept into our equation, we get y=0x-6, or y=-6. We can test this by putting in both points: when x=1, y=-6; and when x=5, y=-6. Therefore, we know we have the right answer.