Question

george is drafting his dissertation paper for his doctoral program. the graph below shows a linear model for the data recorded on the number of pages of the dissertation written as a function of the number of hours george spends on the draft each week. select the equation for the linear model shown. a. $y = \frac{1}{2}x + 4$ b. $y = \frac{2}{3}x + 4$ c. $y = \frac{3}{2}x + 4$ d. $y = 2x + 4$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 4)$, so $b=4$.

Step2: Calculate slope m

Use two points on the line, e.g., $(0,4)$ and $(6,10)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-4}{6-0}=\frac{6}{6}=1$? No, correct point: use $(6,10)$ is not on line, use $(9,10)$? No, use $(0,4)$ and $(12,12)$:
$m=\frac{12-4}{12-0}=\frac{8}{12}=\frac{2}{3}$

Step3: Write linear equation

Linear form: $y=mx+b$, substitute $m=\frac{2}{3}$, $b=4$.
$y=\frac{2}{3}x+4$

Answer:

B. $y = \frac{2}{3}x + 4$