What is the slope intercept form of the line with a slope of $- \frac{2}{3}$ $-2/3$ that passes through $(- 5, 2)$ $(-5,2)$ ?

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What is the slope intercept form of the line with a slope of $- \frac{2}{3}$ $-2/3$ that passes through $(- 5, 2)$ $(-5,2)$ ?

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Answer 1 · 2018-03-05T14:41:52

$y = - \frac{2}{3} x - \frac{4}{3}$ $y=-2/3x-4/3$

Explanation:

$the equation of a line in slope-intercept form$ $"the equation of a line in "color(blue)"slope-intercept form"$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$here m = - \frac{2}{3}$ $"here "m=-2/3$

$\Rightarrow y = - \frac{2}{3} x + b \leftarrow is the partial equation$ $rArry=-2/3x+blarrcolor(blue)"is the partial equation"$

$to find b substitute (- 5, 2) into the partial equation$ $"to find b substitute "(-5,2)" into the partial equation"$

$2 = \frac{10}{3} + b \Rightarrow b = \frac{6}{3} - \frac{10}{3} = - \frac{4}{3}$ $2=10/3+brArrb=6/3-10/3=-4/3$

$\Rightarrow y = - \frac{2}{3} x - \frac{4}{3} \leftarrow in slope-intercept form$ $rArry=-2/3x-4/3larrcolor(red)"in slope-intercept form"$

Answer 2 · 2018-03-05T14:43:41

$y = - \frac{2}{3} x - \frac{4}{3}$ $y= -2/3 x -4/3$

Explanation:

$S l o p e = m$ $color(blue)(Slope = m)$

$\Rightarrow - \frac{2}{3} = \frac{y - y_{1}}{x - x_{1}}$ $color(blue)(=> -2/3 = (y-y_1)/(x-x_1))$

Here $x_{1} = - 5$ $color(red)(x_1=-5)$

And $y_{1} = 2$ $color(red)(y_1=2)$

Put them in the above equation

$\Rightarrow - \frac{2}{3} = \frac{y - 2}{x - (- 5)}$ $color(orange)(=> -2/3 = (y-2)/(x-(-5)))$

$\Rightarrow - \frac{2}{3} = \frac{y - 2}{x + 5}$ $color(orange)(=> -2/3 = (y-2)/(x+5))$

Cross-multiply

$\Rightarrow - 2 (x + 5) = 3 (y - 2)$ $color(purple)(=> -2(x+5)=3(y-2))$

$\Rightarrow - 2 x - 10 = 3 y - 6$ $color(purple)(=> -2x -10=3y-6)$

$\Rightarrow 6 - 10 = 2 x + 3 y$ $color(purple)(=> 6-10=2x+3y)$

$\Rightarrow - 4 - 2 x = 3 y$ $color(green)(=> -4-2x=3y)$

$\Rightarrow 3 y = - 2 x - 4$ $color(green)(=> 3y=-2x-4)$

$\Rightarrow y = - \frac{2}{3} x - \frac{4}{3}$ $color(green)(=> y=-2/3 x -4/3)$

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What is the slope intercept form of the line with a slope of $- \frac{2}{3}$ $-2/3$ that passes through $(- 5, 2)$ $(-5,2)$ ?

2 Answers

Explanation:

Explanation:

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What is the slope intercept form of the line with a slope of $- \frac{2}{3}$ $-2/3$ that passes through $(- 5, 2)$ $(-5,2)$ ?