Question

jamal decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches, then throws back into the water. after plotting all his data, he draws a line of best fit. based on the line of best fit, what would you predict to be the length of a catfish that weighed 48 pounds? (scatter plot with line of best fit, points (20,3), (25,12), (30,21) marked on the line)

Explanation:

Step1: Find line slope (2 points)

Use points $(20,3)$ and $(30,21)$.
Slope $m = \frac{21-3}{30-20} = \frac{18}{10} = 1.8$

Step2: Get line equation (slope-intercept)

Use $m=1.8$ and $(20,3)$ in $y=mx+b$.
$3 = 1.8(20) + b$
$3 = 36 + b$
$b = 3 - 36 = -33$
Equation: $y = 1.8x - 33$

Step3: Solve for $x$ when $y=48$

Substitute $y=48$ into the line equation.
$48 = 1.8x - 33$
$1.8x = 48 + 33$
$1.8x = 81$
$x = \frac{81}{1.8} = 45$

Answer:

45 inches