Let's analyze Samuel's steps to identify any errors:
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Step 1: Calculate the slope (m)
Samuel used the points (-5, 5) and (-3, -3) to calculate the slope: \[ m = \frac{-3 - 5}{-3 - (-5)} = \frac{-8}{2} = -4 \] This calculation is correct. He properly identified the coordinates of the two points and applied the slope formula. -
Step 2: Using the slope and one point to find b
He used the point (-5, 5) to find the y-intercept (b): \[ 5 = -4(-5) + b \ 5 = 20 + b \ b = 5 - 20 \ b = -15 \] Here, Samuel correctly substituted the slope (m = -4) and the coordinates (-5, 5), but he made an arithmetic error in his subtraction from \(5 - 20\), which should give \(b = -15\) correctly (this part is accurate). -
Step 3: Write the equation in slope-intercept form
He wrote the equation of the line as: \[ y = -4x - 15 \] It appears there is a mistake in this equation. He initially wrote \(y = -15x - 4\) which doesn't match the correct slope and intercept values.
From this analysis, the correct response is:
In step 3, he substituted the wrong values for m and b.
The correct equation should be \(y = -4x - 15\), not the one he wrote.