Answer: Linear
The equation is y = 2x-5
Slope = 2
y intercept = -5
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Explanation:
Each time x goes up by 1, y increases by 2. This directly leads to a linear equation due to the same rate of change no matter where you are in the table.
The slope is rise/run = 2/1 = 2 because "y increases by 2 each time x increases by 1".
We could use the slope formula to see this. Pick on any two rows to plug in the coordinates. I'll use the last two rows
m = (y2-y1)/(x2-x1)
m = (3-1)/(4-3)
m = 2/1
m = 2
This confirms the slope is 2.
The positive slope means that the line goes uphill as you move from left to right.
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The y intercept is b = -5 because the y intercept always happens when x = 0. This applies to any function, whether it's linear or not.
Together with m = 2 as the slope and b = -5 as the y intercept, we go from y = mx+b to y = 2x-5 as our linear equation
As a way to check, plug in something like x = 1 to find that...
y = 2x-5
y = 2*1-5
y = 2-5
y = -3
The table shows that x = 1 and y = -3 pair up together in the same row, so that confirms x = 1. I'll let you verify the other x values.
Answer:
Simplifying
x = 11
Step-by-step explanation:
Simplifying
6x + -27 = 39
Reorder the terms:
-27 + 6x = 39
Solving
-27 + 6x = 39
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '27' to each side of the equation.
-27 + 27 + 6x = 39 + 27
Combine like terms: -27 + 27 = 0
0 + 6x = 39 + 27
6x = 39 + 27
Combine like terms: 39 + 27 = 66
6x = 66
Divide each side by '6'.
x = 11
Simplifying
x = 11
Answer:
d = 1 7/24 or 31/24; midpoint would be half of that,or 31/48
Step-by-step explanation:
Since distance is absolute value, add 2/3 and 5/8 to get the entire distance. Midpoint is that distance divided by 2.