TheAnimeGirl
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Heya!
- If the line y = mx + c passes through the point of intersection of the lines x - 2y = -1 and y = 2 and is perpendicular to the line y = 4x + 8 , then find the values of m and c.

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Sagot :

ItsYourDeepak254

Answer:

Hey There!

Let's solve...

We know that the given line is

[tex]y = 4x + 8 \\ [/tex]

Slope is

[tex]m_{g} = 4 \\ [/tex]

The answer is perpendicular to m which is the negative reciprocal of m_g

[tex]m = - \frac{1}{ m_{g} } = - \frac{1}{4} \\ [/tex]

[tex]y = 2 \\ x = 2(2) = - 1 \\ x = 4 - 1 = 3 \\ x = 3[/tex]

The intersection point is

(3,2)

If we substitute the point into

[tex]y = mx + c \\ y = - \frac{1}{4}x + c \\ [/tex]

Now let's solve y intercept...

[tex]2 = - \frac{1}{4}(3) + c \\ \\ c = 2 + \frac{3}{4} \\ [/tex]

[tex] = \frac{8}{4} + \frac{3}{4} \\ \\ = \frac{8 + 3}{4} = \frac{11}{4} [/tex]

Now the required lines are

[tex]y = - \frac{1}{4}x + \frac{11}{4} \\ \\ m = - \frac{1}{4} \\ \\ c = \frac{11}{4} [/tex]

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