#21. Equation of the Line that is Perpendicular to the Line 2x - 3y = 7 and Passes through (1,4) | Summary and Q&A

TL;DR

This content explains how to find the equation of a line that is perpendicular to a given line and passes through a given point.

Key Insights

• 🫥 Finding the equation of a line perpendicular to a given line involves negating and reciprocating the slope.
• 😥 The point-slope formula is used to derive the equation using a known point on the line.
• 🧑‍🏭 Dividing by a common factor can be used to simplify the equation and remove fractions.

Transcript

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Questions & Answers

Q: How do you find the slope of the new line?

The slope of the new line is the negative reciprocal of the slope of the given line, so if the given slope is m, the new slope is -1/m.

Q: What is the point-slope formula?

The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a given point on the line and m is its slope.

Q: Why does dividing by 2 eliminate the fractions in the equation?

Dividing by 2 eliminates the fractions because it cancels out the denominator of the fraction and simplifies the expression to have integer coefficients.

Q: How is the final equation derived?

By simplifying the expression obtained after applying the point-slope formula and dividing by 2, the final equation is y = -3/2x + 11/2.

Summary & Key Takeaways

• The problem is to find the equation of a line that is perpendicular to the line 2x - 3y = 7 and passes through the point (1,4).

• To find the slope of the new line, the slope of the given line is negated and reciprocated (-3/2 becomes 2/3).

• By using the point-slope formula, the equation is derived as y = -3/2x + 11/2.