Question

1. what is the slope of the graph of $y = \frac{1}{3}x - 2$?
2. what is the slope of the graph of $y=-0.7x + 20$?
3. graph the portion of $y = 0.2x + 1$ that lies in the first quadrant using the slope and y - intercept.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find slope for $y=\frac{1}{3}x - 2$

Comparing $y=\frac{1}{3}x - 2$ with $y = mx + b$, we get $m=\frac{1}{3}$.

Step3: Find slope for $y=-0.7x + 20$

Comparing $y=-0.7x + 20$ with $y = mx + b$, we get $m=-0.7$.

Step4: Graph $y = 0.2x+1$ in first quadrant

1. Identify the y - intercept: For $y = 0.2x + 1$, when $x = 0$, $y=1$. So the y - intercept is the point $(0,1)$.
2. Use the slope: The slope $m = 0.2=\frac{1}{5}$. From the point $(0,1)$, move 5 units to the right and 1 unit up to get another point $(5,2)$. Plot the points $(0,1)$ and $(5,2)$ and draw the line segment in the first quadrant.

Answer:

1. The slope is $\frac{1}{3}$.
2. The slope is $-0.7$.
3. Plot the y - intercept $(0,1)$ and use the slope $\frac{1}{5}$ to find another point $(5,2)$ and draw the line segment in the first quadrant.