Alejandro made an error in the steps when determining the equation of the line that is perpendicular to the line 4x−3y=−8 and passes through the point (3,−2). Step Alejandro's Work 1 The equation written in slope-intercept form is y is equal to 4 thirds x plus 8 thirds , which has a slope of 4 thirds 2 The slope of the line perpendicular to the given line is negative 4 thirds 3 Substituting the point and the new slope into point-slope form results in y minus negative 2 is equal to negative 4 thirds times open paren x minus 3 close paren 4 Simplifying, the equation of the line is y plus 2 is equal to negative 4 thirds times open paren x minus 3 close paren Alejandro made his first error in which step?
Rewrite 4x − 3y = −8 in slope-intercept form: −3y = −4x − 8, so y = (4/3)x + 8/3. The given line’s slope is 4/3, so a perpendicular line must have the negative reciprocal slope, −3/4—not −4/3. Therefore, Alejandro’s first error is Step 2, where he identifies the perpendicular slope.
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