Question

the graph shows the percentage of citizens of a certain country who trust in their government. complete parts a through c below.

a. use the two points whose coordinates are shown to find the point - slope form of the equation of the line that models the percentage of citizens trusting in government, x years after 2003.
(simplify your answer. type your answer in point - slope form. use integers or decimals for any numbers in the equation. round to two decimal places as needed.)

Explanation:

Step1: Identify given points

The two clear points from the graph are $(0, 30)$ and $(20, 10)$, where $x$ is years after 2003, $y$ is percentage trust.

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{10-30}{20-0}=\frac{-20}{20}=-1.00$

Step3: Write point-slope form

Use point $(0,30)$: $y-y_1=m(x-x_1)$
$y-30=-1.00(x-0)$
Or using point $(20,10)$: $y-10=-1.00(x-20)$

Answer:

$y - 30 = -1.00(x - 0)$ (or equivalent form $y - 10 = -1.00(x - 20)$)