Question

write an equation of the line containing the given point and perpendicular to the given line. express your answer in the form y = mx + b. (6,8); 3x + y = 7 the equation of the line is y = \square. (simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find slope of given line

Rewrite $3x + y = 7$ as $y = -3x + 7$, so slope $m_1 = -3$.

Step2: Find perpendicular slope

Perpendicular slope $m_2 = \frac{1}{3}$ (negative reciprocal).

Step3: Substitute point into $y=mx+b$

Use $(6,8)$: $8 = \frac{1}{3}(6) + b$

Step4: Solve for $b$

$8 = 2 + b \implies b = 6$

Step5: Write final equation

Combine $m_2$ and $b$ into $y=mx+b$.

Answer:

$y = \frac{1}{3}x + 6$