Question

write the slope-intercept form of the equation of the line described.

1. through: $(1, -4)$, perp. to $y=\frac{1}{8}x - 2$
2. through: $(-3, -5)$, perp. to $y=-\frac{1}{2}x + 2$
3. through: $(-4, 3)$, perp. to $y=x - 2$
4. through: $(-5, -2)$, perp. to $y=-5x - 4$
5. through: $(-3, -2)$, perp. to $y=-\frac{3}{5}x - 2$
6. through: $(1, 2)$, perp. to $y=-\frac{2}{3}x - 1$

Explanation:

Problem 15

Step1: Find perpendicular slope

Slope of given line: $m_1=\frac{1}{8}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = -8$

Step2: Solve for y-intercept $b$

Use point $(1,-4)$ in $y=mx+b$:
$-4 = -8(1) + b$
$b = -4 + 8 = 4$

Step3: Write final equation

$y = -8x + 4$

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Problem 16

Step1: Find perpendicular slope

Slope of given line: $m_1=-\frac{1}{2}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = 2$

Step2: Solve for y-intercept $b$

Use point $(-3,-5)$ in $y=mx+b$:
$-5 = 2(-3) + b$
$b = -5 + 6 = 1$

Step3: Write final equation

$y = 2x + 1$

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Problem 17

Step1: Find perpendicular slope

Slope of given line: $m_1=1$. Perpendicular slope $m_2 = -\frac{1}{m_1} = -1$

Step2: Solve for y-intercept $b$

Use point $(-4,3)$ in $y=mx+b$:
$3 = -1(-4) + b$
$b = 3 - 4 = -1$

Step3: Write final equation

$y = -x - 1$

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Problem 18

Step1: Find perpendicular slope

Slope of given line: $m_1=-5$. Perpendicular slope $m_2 = -\frac{1}{m_1} = \frac{1}{5}$

Step2: Solve for y-intercept $b$

Use point $(-5,-2)$ in $y=mx+b$:
$-2 = \frac{1}{5}(-5) + b$
$b = -2 + 1 = -1$

Step3: Write final equation

$y = \frac{1}{5}x - 1$

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Problem 19

Step1: Find perpendicular slope

Slope of given line: $m_1=-\frac{3}{5}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = \frac{5}{3}$

Step2: Solve for y-intercept $b$

Use point $(-3,-2)$ in $y=mx+b$:
$-2 = \frac{5}{3}(-3) + b$
$b = -2 + 5 = 3$

Step3: Write final equation

$y = \frac{5}{3}x + 3$

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Problem 20

Step1: Find perpendicular slope

Slope of given line: $m_1=-\frac{2}{3}$. Perpendicular slope $m_2 = -\frac{1}{m_1} = \frac{3}{2}$

Step2: Solve for y-intercept $b$

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

Step3: Write final equation

$y = \frac{3}{2}x + \frac{1}{2}$

Answer:

1. $y = -8x + 4$
2. $y = 2x + 1$
3. $y = -x - 1$
4. $y = \frac{1}{5}x - 1$
5. $y = \frac{5}{3}x + 3$
6. $y = \frac{3}{2}x + \frac{1}{2}$