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2 years ago

I need help with this question

Mathematics

1 answer:

Viefleur [7K]2 years ago

4 0

Answer:

m = -1

Step-by-step explanation:

m = (1 - 3) / (4-2)

m = -2/2

m = -1

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Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).

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The equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$

Explanation:

The equation of the line is perpendicular to $y=-14 x-8$

The equation is of the form $y=mx+b$ where m=-14

<u>Slope:</u>

The slope of the perpendicular line can be determined using the formula,

$m_1 \cdot m_2=-1$

$-14 \cdot m_2=-1$

$m_2=\frac{1}{14}$

Thus, the slope of the line is $m=\frac{1}{14}$

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the slope $m=\frac{1}{14}$ and the point (2,-4), we get,

$y+4=\frac{1}{14}(x-2)$

Simplifying, we get,

$y+4=\frac{1}{14}x-\frac{1}{7}$

$y=\frac{1}{14}x-\frac{1}{7}-4$

$y=\frac{1}{4}x-\frac{29}{7}$

Thus, the equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$

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