Question

2 - 26. in the lesson 2.1.3a resource page, graph a - line to
a. a line that goes up 3 each time it goes over 5.
b. a line with δx = 4 and δy=-6.
c. a line with δy = δx.
d. a line that has δy = 3 and δx = 0.

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the $y$ - value and $\Delta x$ is the change in the $x$ - value.

Step2: Graph for part a

The slope $m = \frac{3}{5}$. Start at a point (e.g., the origin $(0,0)$). Move 5 units to the right (increase $x$ by 5) and 3 units up (increase $y$ by 3) to get another point. Then draw a line through these two points.

Step3: Graph for part b

The slope $m=\frac{\Delta y}{\Delta x}=\frac{-6}{4}=-\frac{3}{2}$. Start at a point (say $(0,0)$). Move 4 units to the right (increase $x$ by 4) and 6 units down (decrease $y$ by 6) to get a new point. Draw a line through the starting - point and the new point.

Step4: Graph for part c

Since $\Delta y=\Delta x$, the slope $m = 1$. Start at a point (e.g., $(0,0)$). Move 1 unit to the right and 1 unit up to get another point. Draw a line through these points.

Step5: Graph for part d

The slope $m=\frac{\Delta y}{\Delta x}=\frac{3}{0}$, which is undefined. This represents a vertical line. If $\Delta x = 0$, the line is vertical. You can draw a vertical line passing through any $x$ - value (since $\Delta x=0$ means there is no horizontal change). For example, if we consider a point on the line, say $(x_0,y_0)$ and since $\Delta x = 0$, all points on the line have the same $x$ - coordinate $x_0$.

Answer:

Graphs are drawn as described above for each part (a - d).