To find the slope of a line from a graph, we use the formula:
Slope (m) = Rise / Run
*
Rise: How much the line goes up or down vertically.
*
Run: How much the line goes left or right horizontally.
We pick two points on the line where it crosses the grid intersections perfectly to make counting easy. Let's solve each one step-by-step.
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1)
* Pick two points: Let's choose $(-4, 0)$ and $(2, -2)$.
*
Rise: From $y=0$ down to $y=-2$, the change is $-2$.
*
Run: From $x=-4$ to $x=2$, the change is $6$ (count 6 squares to the right).
* Slope = $\frac{-2}{6}$
* Simplify the fraction: $\frac{-1}{3}$
2)
* Pick two points: Let's choose $(0, -4)$ and $(1, -1)$.
*
Rise: From $y=-4$ up to $y=-1$, the change is $+3$.
*
Run: From $x=0$ to $x=1$, the change is $1$.
* Slope = $\frac{3}{1}$
* Answer: $3$
3)
* Pick two points: Let's choose $(-2, 0)$ and $(0, -3)$.
*
Rise: From $y=0$ down to $y=-3$, the change is $-3$.
*
Run: From $x=-2$ to $x=0$, the change is $2$.
* Slope = $\frac{-3}{2}$
* Answer: $-\frac{3}{2}$
4)
* Pick two points: Let's choose $(-2, -3)$ and $(0, 0)$.
*
Rise: From $y=-3$ up to $y=0$, the change is $+3$.
*
Run: From $x=-2$ to $x=0$, the change is $2$.
* Slope = $\frac{3}{2}$
* Answer: $\frac{3}{2}$
5)
* Pick two points: Let's choose $(-2, -3)$ and $(0, 1)$.
*
Rise: From $y=-3$ up to $y=1$, the change is $+4$.
*
Run: From $x=-2$ to $x=0$, the change is $2$.
* Slope = $\frac{4}{2}$
* Simplify: $2$
6)
* Pick two points: Let's choose $(1, -4)$ and $(2, 0)$.
*
Rise: From $y=-4$ up to $y=0$, the change is $+4$.
*
Run: From $x=1$ to $x=2$, the change is $1$.
* Slope = $\frac{4}{1}$
* Answer: $4$
7)
* Pick two points: Let's choose $(0, 4)$ and $(1, 1)$.
*
Rise: From $y=4$ down to $y=1$, the change is $-3$.
*
Run: From $x=0$ to $x=1$, the change is $1$.
* Slope = $\frac{-3}{1}$
* Answer: $-3$
8)
* Pick two points: Let's choose $(-2, -4)$ and $(0, 0)$.
*
Rise: From $y=-4$ up to $y=0$, the change is $+4$.
*
Run: From $x=-2$ to $x=0$, the change is $2$.
* Slope = $\frac{4}{2}$
* Simplify: $2$
Final Answer:
1) -1/3
2) 3
3) -3/2
4) 3/2
5) 2
6) 4
7) -3
8) 2
Parent Tip: Review the logic above to help your child master the concept of kuta worksheet.
