Question

1. write an equation in slope - intercept form for a line perpendicular to the equation y = -3x + 7 and contains the point (9, 6)

Explanation:

Step1: Find perpendicular slope

The slope of $y=-3x+7$ is $m_1=-3$. The slope of a perpendicular line is the negative reciprocal: $m_2 = \frac{1}{3}$

Step2: Substitute point into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{3}$, $x=9$, $y=6$:
$6 = \frac{1}{3}(9) + b$

Step3: Solve for y-intercept $b$

Simplify and isolate $b$:
$6 = 3 + b$
$b = 6 - 3 = 3$

Step4: Write final equation

Substitute $m=\frac{1}{3}$ and $b=3$ into $y=mx+b$.

Answer:

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