Question

at the start of summer vacation, wesley decides to learn a number of kanji characters each week. the total number of characters wesley knows, y, is a function of the number of weeks, x. the graph of the function passes through the points (3, 120) and (5, 160). find and describe the rate of change of the function. the rate of change is 20. it represents the number of characters wesley learns each week. find and describe the initial value of the function. the initial value is

Explanation:

Step1: Find the slope - intercept form equation

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). We know $m = 20$ (from the previous part). Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(3,120)$ and $m = 20$.
$y-120 = 20(x - 3)$

Step2: Expand and solve for $b$

Expand the right - hand side: $y-120=20x-60$. Then, add 120 to both sides to get $y = 20x+60$. When $x = 0$ (initial value), $y=b$.

Answer:

60