Question

a line is graphed below. select the correct answer in each drop - down that makes each statement true. the slope of the line is and the equation is. the line to the x - axis and it a function. the domain is and the range is

Explanation:

Step1: Recall slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line like the one in the graph, if we take two points, say $(- 10,5)$ and $(10,5)$, then $m=\frac{5 - 5}{10-(-10)} = 0$.

Step2: Determine line - equation form

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since $m = 0$ and the line intersects the y - axis at $y = 5$, the equation is $y=0x + 5$ or $y = 5$.

Step3: Analyze relation to x - axis

A horizontal line is parallel to the x - axis.

Step4: Check if it's a function

For every x - value in the domain, there is exactly one y - value. So, it is a function.

Step5: Find domain and range

The line extends infinitely in the x - direction, so the domain is all real numbers, $(-\infty,\infty)$. The y - value is always 5, so the range is $\{5\}$.

Answer:

The slope of the line is 0 and the equation is $y = 5$.
The line is parallel to the x - axis and it is a function.
The domain is $(-\infty,\infty)$ and the range is $\{5\}$.