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.)
y - 24 = - 0.833(x - 4)
b. write the equation in part (a) in slope - intercept form. use function notation, where f(x) is the percentage of citizens trusting in government x years after 2003.
f(x) =
(simplify your answer. use integers or decimals for any numbers in the expression. round to two decimal places as needed.)

Explanation:

Step1: Identify two points

From the graph, the points are $(4, 24)$ and $(16, 14)$.

Step2: Calculate the slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{14-24}{16-4}=\frac{-10}{12}\approx-0.83$

Step3: Write point-slope form

Using point $(4,24)$: $y - y_1 = m(x - x_1)$
$y - 24 = -0.83(x - 4)$

Step4: Convert to slope-intercept form

Expand and solve for $y$:
$y - 24 = -0.83x + 3.32$
$y = -0.83x + 3.32 + 24$
$y = -0.83x + 27.32$
Rewrite in function notation: $f(x)=-0.83x + 27.32$

Answer:

a. $y - 24 = -0.83(x - 4)$
b. $f(x)=-0.83x + 27.32$