Question

Question #ba70b

Answer 1

Problem 1

Let `{((x_1,y_1)=(3,5)),((x_2,y_2)=(-9,5)):}`

By Slope Formula,

`m={y_2-y_1}/{x_2-x_1}={5-5}/{-9-3}=0`

By Point-Slope Form `y-y_1=m(x-x_1)`, we have the equation

`y-5=0(x-3)=0 => y=5`

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Problem 2

Let `(x_1,y_1)=(2, (2)^3-10)=(2,-2)`

By rewriting the equation in Slope-Intercept Form,

`3x-2y+5=0 => y=3/2x+5/2 =>` Slope `=3/2`

By taking the negative reciprocal (since perpendcular),

`m=-2/3`

By Point-Slope Form, we have the equation

`y+2=-2/3(x-2)`

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Problem 3

By setting `y=0`, we can find the `x`-intercept,

`0=5x-75 => x=15 =>` Let `(x_1,y_1)=(15,0)`

By rewriting in Slope-Intercept Form,

`7y-5x=70 => y=5/7x+10 => m=5/7`

By Point-Slope Form, we have the equation

`y=5/7(x-15)`

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I hope that this was helpful.