Question

1. write the equation of a line perpendicular to $y=-2x+1$ that passes through the point (2, 3).

a $y=-2x+7$
b $y=\frac{1}{2}x+\frac{1}{2}$
c $y=\frac{1}{2}x+2$
d $y=-2x+8$

1. write the equation of a line perpendicular to $y=\frac{1}{3}x-9$ that passes through the point (-6, 10).

a $y=-3x-8$
b $y=\frac{1}{3}x-9$
c $y=\frac{1}{3}x+10$
d $y=-3x+6$

1. a line is perpendicular to $y=2x-7$

what is the slope of this line?
a -2
b 2
c -1/2
d 1/2

1. what slope is perpendicular to:

$m=5/8$
a 8/5
b -8/5
c 5/8
d -5/8

Explanation:

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Problem 4

Step1: Find perpendicular slope

The slope of $y=-2x+1$ is $m_1=-2$. Perpendicular slope $m_2 = \frac{1}{2}$ (negative reciprocal).

Step2: Solve for y-intercept b

Use point $(2,3)$ in $y=\frac{1}{2}x+b$:
$3 = \frac{1}{2}(2) + b$
$3 = 1 + b$
$b=2$

Step3: Form final equation

$y=\frac{1}{2}x+2$

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Problem 5

Step1: Find perpendicular slope

The slope of $y=\frac{1}{3}x-9$ is $m_1=\frac{1}{3}$. Perpendicular slope $m_2=-3$ (negative reciprocal).

Step2: Solve for y-intercept b

Use point $(-6,10)$ in $y=-3x+b$:
$10 = -3(-6) + b$
$10 = 18 + b$
$b=-8$

Step3: Form final equation

$y=-3x-8$

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Problem 6

Step1: Find perpendicular slope

The slope of $y=2x-7$ is $m_1=2$. Perpendicular slope is negative reciprocal: $m_2=-\frac{1}{2}$

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Problem 7

Step1: Find perpendicular slope

Given $m=\frac{5}{8}$, perpendicular slope is negative reciprocal: $m_2=-\frac{8}{5}$

Answer:

1. C. $y = \frac{1}{2}x + 2$
2. A. $y = -3x - 8$
3. C. -1/2
4. B. -8/5