Question

part a what is the slope of the line? enter the answer in the box. the slope is part b what is the value of x? enter the answer in the box. x = christopher jarrell rimmer, id #****39 growth math 6+ mi 2010 1.1 question # 18

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 given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, the two - points are $(0,0)$ and $(x, - 10)$. So $m=\frac{-10 - 0}{x-0}=-\frac{10}{x}$.

Step2: Determine slope from graph

From the right - triangle on the graph, the vertical change (rise) is $- 10$ and the horizontal change (run) is $x$. The slope of the line is the ratio of the rise to the run.
If we assume the line is in the form $y = mx + b$ and the line passes through the origin $(0,0)$ and another point $(x,-10)$.
For part A:
The slope of the line passing through $(0,0)$ and $(x,-10)$ is $m =-\frac{10}{x}$. If we consider the ratio of the vertical and horizontal sides of the right - triangle formed by the line, the slope $m=-\frac{10}{5}=-2$ (assuming from the triangle that the horizontal side length is 5, since the vertical side is 10).
For part B:
We know the slope $m = - 2$ and the line passes through $(0,0)$ and $(x,-10)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $m=-2$, $y_1 = 0$, $y_2=-10$, $x_1 = 0$, we have $-2=\frac{-10 - 0}{x-0}$. Cross - multiplying gives $-2x=-10$, so $x = 5$.

Answer:

Part A: - 2
Part B: 5