Question

a procedure allows a researcher to determine the concentration of glucose y, in micrograms per milliliter (μg/ml), in a soil sample by measuring the absorbance, x, at a specific wavelength of light. the scatterplot shows this relationship for 5 soil samples. which equation is the most appropriate linear model for the data? a. y = 1.5+90x b. y = 1.5+10x c. y = 10+1.5x d. y = 90+1.5x question 2(1 point) the graph of linear function f is shown. what is the y - intercept of the graph of f? a. (0,0) b. (0,2) c. (0,3) d. (0,6)

Explanation:

Step1: Recall linear - equation form

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze the first scatter - plot for slope and y - intercept

For the scatter - plot of glucose concentration vs absorbance:

• The y - intercept is the value of $y$ when $x = 0$. Looking at the scatter - plot, when $x=0$, $y$ is around $1.5$.
• To estimate the slope, we can take two points. Let's say $(x_1,y_1)=(0,1.5)$ and $(x_2,y_2)=(0.5,45)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{45 - 1.5}{0.5}=\frac{43.5}{0.5}=87\approx90$. So the equation is $y = 1.5+90x$.

Step3: Analyze the second graph for y - intercept

For the graph of the linear function $f$:
The y - intercept is the point where the line crosses the y - axis. When $x = 0$, from the graph, $y = 2$. The y - intercept is the point $(0,2)$.

Answer:

Question 1: A. $y = 1.5+90x$
Question 2: B. $(0,2)$