Question

1. determine the slope of the line below.
2. what is the slope of the graph of y = 1/3x - 2?
3. what is the slope of the graph of y = -0.7x + 20?
4. graph the portion of y = 0.2x + 1 that lies in the first quadrant using the slope and y - intercept.

Explanation:

Step1: Select two points on the line

Let's take the points $(0,8)$ and $(8,5)$.

Step2: Use slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 8,x_2=8,y_2 = 5$. Then $m=\frac{5 - 8}{8 - 0}=\frac{-3}{8}=- 0.375$.

Step3: For $y=\frac{1}{3}x - 2$

The equation of a line is in the form $y=mx + b$, where $m$ is the slope. So the slope is $\frac{1}{3}$.

Step4: For $y=-0.7x + 20$

Using the form $y = mx + b$, the slope $m=-0.7$.

Step5: For $y = 0.2x+1$

The $y$-intercept is $b = 1$ (when $x = 0,y=1$). The slope $m = 0.2=\frac{1}{5}$. To graph in the first - quadrant, find the $x$-intercept by setting $y = 0$. So $0=0.2x + 1$, then $0.2x=-1,x=-5$. But we are interested in the first - quadrant. We can start at the point $(0,1)$ (the $y$-intercept) and then use the slope. Since the slope is $\frac{1}{5}$, for every 5 units we move to the right (increase in $x$), we move 1 unit up (increase in $y$). We can plot points like $(0,1),(5,2),(10,3)$ etc. in the first - quadrant.

Answer:

1. The slope of the line is $-0.375$.
2. The slope of the graph of $y=\frac{1}{3}x - 2$ is $\frac{1}{3}$.
3. The slope of the graph of $y=-0.7x + 20$ is $-0.7$.
4. The slope of $y = 0.2x + 1$ is $0.2$, and to graph in the first - quadrant, start at the $y$-intercept $(0,1)$ and use the slope to find other points like $(5,2),(10,3)$ etc.