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, y, 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

Points: $(4, 27)$ and $(18, 18)$

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$$m=\frac{18-27}{18-4}=\frac{-9}{14}\approx-0.64$$

Step3: Write point-slope form

Using point $(4,27)$: $y-y_1=m(x-x_1)$
$$y-27=-0.64(x-4)$$
(Using point $(18,18)$ is also valid: $y-18=-0.64(x-18)$)

Answer:

$y - 27 = -0.64(x - 4)$ (or $y - 18 = -0.64(x - 18)$)