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: Calculate the slope

The two points are $(4,23)$ and $(16,14)$. The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{14-23}{16-4}=\frac{-9}{12}=-0.75$

Step2: Write point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(4,23)$ as $(x_1,y_1)$.
$y-23=-0.75(x-4)$
(Alternatively, using $(16,14)$: $y-14=-0.75(x-16)$ is also valid)

Answer:

$y-23=-0.75(x-4)$ (or $y-14=-0.75(x-16)$)