How to help your Students Learn Slope - RETHINK Math Teacher - Free Printable

To find the slope each tank must use, we need to calculate the "rise over run" between the tank's position and the alien it is targeting.

The formula for slope ($m$) is:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Where $(x_1, y_1)$ is the starting point (the tank) and $(x_2, y_2)$ is the ending point (the alien).

Let's break down each tank one by one.

Tank 1
* Target: The red multi-eyed alien.
* Tank Position: Looking at the bottom of the grid, Tank 1 is at $x = 3$, $y = -7$. So, $(3, -7)$.
* Alien Position: The red alien is at $x = 4$, $y = 4$. So, $(4, 4)$.
* Calculation:
* Change in $y$ (Rise): $4 - (-7) = 4 + 7 = 11$
* Change in $x$ (Run): $4 - 3 = 1$
* Slope: $\frac{11}{1} = 11$

Tank 2
* Target: The green one-eyed alien.
* Tank Position: Tank 2 is at $x = 6$, $y = -7$. So, $(6, -7)$.
* Alien Position: The green alien is at $x = 2$, $y = 1$. So, $(2, 1)$.
* Calculation:
* Change in $y$ (Rise): $1 - (-7) = 1 + 7 = 8$
* Change in $x$ (Run): $2 - 6 = -4$
* Slope: $\frac{8}{-4} = -2$

Tank 3
* Target: The pink octopus alien.
* Tank Position: Tank 3 is at $x = -6$, $y = -7$. So, $(-6, -7)$.
* Alien Position: The pink alien is at $x = -6$, $y = -2$. So, $(-6, -2)$.
* Calculation:
* Change in $y$ (Rise): $-2 - (-7) = -2 + 7 = 5$
* Change in $x$ (Run): $-6 - (-6) = -6 + 6 = 0$
* Slope: $\frac{5}{0}$
* Division by zero is undefined. This means the line is vertical. The slope is Undefined.

Tank 4
* Target: The purple one-eyed alien.
* Tank Position: Tank 4 is at $x = -4$, $y = -7$. So, $(-4, -7)$.
* Alien Position: The purple alien is at $x = -5$, $y = 5$. So, $(-5, 5)$.
* Calculation:
* Change in $y$ (Rise): $5 - (-7) = 5 + 7 = 12$
* Change in $x$ (Run): $-5 - (-4) = -5 + 4 = -1$
* Slope: $\frac{12}{-1} = -12$

Final Answer:
Tank 1: 11
Tank 2: -2
Tank 3: Undefined
Tank 4: -12