Question

some questions...

1. what is the slope of the line y = 5?
2. what is the slope of the line x = -2?
3. what is the slope of the line x = 0?
4. what is the difference between the graphs y = 3 and y = 3x? graph both below and explain.

(there are two grid graphs in the original image, which are omitted here)

Explanation:

Step1: Identify line type for $y=5$

$y=5$ is a horizontal line. Slope of horizontal lines is $0$.

Step2: Identify line type for $x=-2$

$x=-2$ is a vertical line. Slope of vertical lines is undefined.

Step3: Identify line type for $x=0$

$x=0$ is the y-axis, a vertical line. Slope is undefined.

Step4: Analyze graphs for $y=3$ and $y=3x$

• $y=3$: Horizontal line, slope $0$, $y$-intercept at $(0,3)$.
• $y=3x$: Linear line, slope $3$, passes through origin $(0,0)$.

Graph details:

• For $y=3$: Plot points like $(-2,3)$, $(0,3)$, $(2,3)$ and draw a horizontal line through them.
• For $y=3x$: Plot points like $(-1,-3)$, $(0,0)$, $(1,3)$ and draw a straight line through them.

Difference: $y=3$ is horizontal (constant value, no change in $y$ with $x$), $y=3x$ is a slanted line passing through the origin, with $y$ increasing 3 units for every 1 unit increase in $x$.

Answer:

1. $0$
2. Undefined
3. Undefined

14.

• Graph of $y=3$: Horizontal line through $(0,3)$; graph of $y=3x$: Straight line through $(0,0)$ with slope 3.
• Difference: $y=3$ is a horizontal constant line (slope 0), while $y=3x$ is a slanted line passing through the origin (slope 3) that changes with $x$.