How do you write an equation of a line given (9,3) and m=-2/3?

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Answer 1 · 2017-01-16T02:52:37

Use the point-slope formula. See below:

The point-slope formula states: $(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))$

Where $color(blue)(m)$ is the slope and $color(red)(((x_1, y_1)))$ is a point the line passes through.

Substituting the point and slope from the problem gives the equation:

$(y - color(red)(3)) = color(blue)(-2/3)(x - color(red)(9))$

We can also convert to the more familiar slope-intercept form if we solve for $y$ .

The slope-intercept form of a linear equation is:

$y = color(red)(m)x + color(blue)(b)$

Where $color(red)(m)$ is the slope and $color(blue)(b$ is the y-intercept value.

$y - color(red)(3) = (color(blue)(-2/3) xx x) - (color(blue)(-2/3) xx color(red)(9))$

$y - color(red)(3) = -2/3x - (-6)$

$y - color(red)(3) = -2/3x + 6$

$y - color(red)(3) + 3 = -2/3x + 6 + 3$

$y - 0 = -2/3x + 9$

$y = -2/3x + 9$