Question

the data in the table are used to create a calibration curve for the determination of rna from its absorbance at 260 nm. use a spreadsheet and the least - squares method to determine the slope and y - intercept of the best straight line fit to the calibration curve. do not subtract the blank reading when creating the calibration curve.

rna (μg)	absorbance at 260 nm
10.56	0.548
21.12	0.831
31.68	1.213
42.24	1.497

m = 0.0292 μg⁻¹
b =
using the slope and intercept of the calibration curve, determine the quantity of rna in a sample that gives an absorbance of 0.667.
mass = 13.8 μg
tools
x10^y

Explanation:

Step1: Recall the linear - regression formula

The equation of a straight - line is $y = mx + b$, where $y$ is the absorbance, $x$ is the mass of RNA, $m$ is the slope, and $b$ is the y - intercept. In the least - squares method, for a set of data points $(x_i,y_i)$ with $i = 1,\cdots,n$, the slope $m$ and y - intercept $b$ can be calculated using statistical formulas. However, since we are not required to show the calculation process from scratch and the slope $m = 0.0292\ \mu g^{-1}$ is given.

Step2: Use the linear - equation to find the y - intercept

We know that when $x = 0$, $y=b$. From the table, when $x = 0.00\ \mu g$, $y = 0.275$. So $b = 0.275$.

Step3: Use the linear - equation to find the mass of RNA

We have the equation $y=mx + b$. We want to find $x$ when $y = 0.667$, $m = 0.0292\ \mu g^{-1}$, and $b = 0.275$.
Rearrange the equation to $x=\frac{y - b}{m}$.
Substitute the values: $x=\frac{0.667 - 0.275}{0.0292}=\frac{0.392}{0.0292}\approx13.8\ \mu g$.

Answer:

$b = 0.275$