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The equation for line pp can be written as y=97x−9y= \frac{9}{7}x-9. Line qq is perpendicular to line pp and passes through (9,−6)(9, -6). What is the equation of line qq? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Full solution

Q. The equation for line pp can be written as y=97x−9y= \frac{9}{7}x-9. Line qq is perpendicular to line pp and passes through (9,−6)(9, -6). What is the equation of line qq? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Line p's Equation: Line p's equation is y=97x−9y = \frac{9}{7}x - 9. The slope of line p is 97\frac{9}{7}.
  2. Perpendicular Line Slope: Line qq is perpendicular to line pp, so its slope is the negative reciprocal of 97\frac{9}{7}, which is −79-\frac{7}{9}.
  3. Calculate Y-Intercept: Using the point (9,−6)(9, -6) and the slope −79-\frac{7}{9}, plug into y=mx+by = mx + b to find bb, the y-intercept of line qq.\newline−6=(−79)⋅9+b-6 = \left(-\frac{7}{9}\right)\cdot9 + b
  4. Simplify Equation: Simplify the equation: −6=−7+b-6 = -7 + b.
  5. Solve for Y-Intercept: Add 77 to both sides to solve for bb: b=1b = 1.
  6. Final Equation of Line q: The equation of line q in slope-intercept form is y=−79x+1y = -\frac{7}{9}x + 1.

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