Question

question 5
write the equation of a line through (2, -3), perpendicular to $y = \frac{1}{3}x$
$y = \square x + \square$
question 6
write the equation of a line through (-1, -5), perpendicular to $y = \frac{1}{9}x + 5$
$y = \square x + \square$

Explanation:

Question 5

Step1: Find perpendicular slope

The slope of $y=\frac{1}{3}x$ is $m_1=\frac{1}{3}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = -3$.

Step2: Solve for y-intercept b

Use point $(2,-3)$ in $y=mx+b$:
$-3 = -3(2) + b$
$-3 = -6 + b$
$b = -3 + 6 = 3$

Question 6

Step1: Find perpendicular slope

The slope of $y=\frac{1}{9}x+5$ is $m_1=\frac{1}{9}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = -9$.

Step2: Solve for y-intercept b

Use point $(-1,-5)$ in $y=mx+b$:
$-5 = -9(-1) + b$
$-5 = 9 + b$
$b = -5 - 9 = -14$

Answer:

Question 5: $y = -3x + 3$
Question 6: $y = -9x - 14$