Alejandro made an error in the steps below when determining the equation of the line that is perpendicular to the line 4x – 3y = -8 and passes through the point (3, -2). 1. The equation written in slope-intercept form is y = 4/3x + 8/3, which has a slope of 4/3. 2. The slope of the line perpendicular to the given line is -4/3. 3. Substituting the point and the new slope into point-slope form results in y – (-2) = -4/3(x – 3). 4. Simplifying, the equation of the line is y + 2 = -4/3(x – 3). Alejandro made his first error in which step

Alejandro made his first error in Step 1.

Here’s why: The slope of the line given by the equation (4x – 3y = -8) needs to be found correctly in slope-intercept form (y = mx + b).

Rearranging gives:

[

3y = 4x + 8 quad Rightarrow quad y = frac{4}{3}x + frac{8}{3}

]

Thus, the slope from the original line is actually (frac{4}{3}), but the slope of the line perpendicular to it should be (-frac{3}{4}) (not (-frac{4}{3}) as stated in Step 2).

So, the incorrect slope in Step 2 is a continuation of the error from Step 1.

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