in exercises 1 - 4, describe the slope of the line. then find the slope. (see example 1.) 2. 3. 4.

Question

Accepted Answer

1. **For the first - line with points $(2,-2)$ and $(-3,1)$**:
   - **Explanation**:
     - **Step 1: Identify the slope formula**
The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, let $(x_1,y_1)=(2,-2)$ and $(x_2,y_2)=(-3,1)$.
     - **Step 2: Substitute the values into the formula**
$$
\begin{align*}
m&=\frac{1-(-2)}{-3 - 2}\
&=\frac{1 + 2}{-3-2}\
&=\frac{3}{-5}\
&=-\frac{3}{5}
\end{align*}
$$
   - **Answer**: The slope of the line is $-\frac{3}{5}$.
2. **For the second - line with points $(1,-1)$ and $(4,3)$**:
   - **Explanation**:
     - **Step 1: Identify the slope formula**
Using $m=\frac{y_2 - y_1}{x_2 - x_1}$, let $(x_1,y_1)=(1,-1)$ and $(x_2,y_2)=(4,3)$.
     - **Step 2: Substitute the values into the formula**
$$
\begin{align*}
m&=\frac{3-(-1)}{4 - 1}\
&=\frac{3 + 1}{4-1}\
&=\frac{4}{3}
\end{align*}
$$
   - **Answer**: The slope of the line is $\frac{4}{3}$.
3. **For the third - line with points $(-1,-4)$ and $(0,-1)$**:
   - **Explanation**:
     - **Step 1: Identify the slope formula**
Using $m=\frac{y_2 - y_1}{x_2 - x_1}$, let $(x_1,y_1)=(-1,-4)$ and $(x_2,y_2)=(0,-1)$.
     - **Step 2: Substitute the values into the formula**
$$
\begin{align*}
m&=\frac{-1-(-4)}{0-(-1)}\
&=\frac{-1 + 4}{0 + 1}\
&=\frac{3}{1}\
&=3
\end{align*}
$$
   - **Answer**: The slope of the line is $3$.
4. **For the fourth - line with points $(5,-1)$ and $(0,3)$**:
   - **Explanation**:
     - **Step 1: Identify the slope formula**
Using $m=\frac{y_2 - y_1}{x_2 - x_1}$, let $(x_1,y_1)=(5,-1)$ and $(x_2,y_2)=(0,3)$.
     - **Step 2: Substitute the values into the formula**
$$
\begin{align*}
m&=\frac{3-(-1)}{0 - 5}\
&=\frac{3 + 1}{0-5}\
&=\frac{4}{-5}\
&=-\frac{4}{5}
\end{align*}
$$
   - **Answer**: The slope of the line is $-\frac{4}{5}$.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: