Question

what is the mistake that julia made when showing her students how to convert an equation of a line in point - slope form to slope - intercept form?
$y - 9 = - 4(x - 3)$
$y - 9 = - 4x - 12$
$y = - 4x - 3$
julia added 3 to both sides of the equation.
julia did not make a mistake.
julia multiplied $(-4)(-3)$ for a product of -12 instead of 12.
julia added 9 to both sides of the equation instead of adding.

Explanation:

Step1: Analyze the distribution step

The original equation is \( y - 9=-4(x - 3) \). When distributing \(-4\) to \((x - 3)\), we should get \( y - 9=-4x+(-4)\times(-3) \). Calculating \((-4)\times(-3)\) gives \( 12 \), but Julia got \(- 12\).

Step2: Evaluate other options

• Option 1: There's no step where 3 is added, so this is incorrect.
• Option 2: Since there is a mistake in the distribution, this is incorrect.
• Option 4: The last step of adding 9 is done correctly (\(y-9 + 9=-4x - 12+9\) gives \(y=-4x - 3\) only because the previous step was wrong), so this is incorrect.

Answer:

Julia multiplied \((-4)(-3)\) for a product of -12 instead of 12. (The option: Julia multiplied \((-4)(-3)\) for a product of -12 instead of 12.)