How do you write an equation of a line given (9,-5), m=-1/3?

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How do you write an equation of a line given (9,-5), m=-1/3?

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Answer 1 · 2017-08-29T20:50:37

$y = - \frac{1}{3} x - 2$ $y=-1/3x-2$

Explanation:

Let the given point be $P_{1} \to (x_{1}, y_{1}) = (9, - 5)$ $P_1->(color(green)(x_1),color(red)(y_1))=(color(green)(9),color(red)(-5))$

Let the gradient be $m = - \frac{1}{3}$ $m=-1/3$

Using the standardised form $y_{1} = m x_{1} + c$ $color(red)(y_1)=mcolor(green)(x_1)+c$

Where $c$ $c$ is a constant

Then by substitution: $- 5 = (- \frac{1}{3}) (9) + c$ $color(red)(-5)=(-1/3)(color(green)(9))+c$

but $- \frac{1}{3} \times 9 = - 3$ $-1/3xx9 = -3$ giving:

$- 5 = 3 + c$ $-5=3+c$

Add $3$ $color(magenta)(3)$ to both sides

$- 5 = - 3 + c dd \to dd - 5 + 3 = - 3 + 3 + c$ $color(green)(-5=-3+c color(white)("dd")->color(white)("dd")-5color(magenta)(+3)=-3color(magenta)(+3)+c)$

$ddddddddddddd \to dddd - 2 d = dddd 0 d + c$ $color(green)(color(white)("ddddddddddddd")-> color(white)("dddd")-2color(white)("d")=color(white)("dddd")0color(white)("d")+c$

Thus $c = - 2$ $c=-2$ so the finished equation is:

$y = - \frac{1}{3} x - 2$ $y=-1/3x-2$

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How do you write an equation of a line given (9,-5), m=-1/3?

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