How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

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How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

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Answer 1 · 2016-07-06T20:43:02

The slope-intercept form of the equation is $y=-2/3x+10/3$

Explanation:

The slope-intercept form of the equation of the line is $y=mx+b$
where $m=$ slope and $b=$ the y intercept

$m=(y_2-y_1)/(x_2-x_1)$

$x_1=2$
$y_1=2$
$x_2=-1$
$y_2=4$

$m = (4-2)/(-1-2)$

$m = (2)/(-3)$

$m=-2/3$

Now use the point slope formula to solve for the equation of the line.

$(y-y_1)=m(x-x_1)$

For this situation we are given the slope of $3$ and a point of $(2,1)$

$m=-2/3$
$x_1=2$
$y_1=2$

$(y-y_1)=m(x-x_1)$

$(y-2)=-2/3(x-2)$

$y-2=-2/3x-4/3$

$y cancel(-2) cancel(+2)=-2/3x+4/3 + 2$

$y=-2/3x+4/3 +6/3$

$y=-2/3x+10/3$

Answer 2 · 2016-07-06T20:53:14

$y = (-2x)/3 +10/3$

Explanation:

If you have two points on a straight line, there is a lovely formula which allows you to get the equation immediately. It is based on the formula for the slope, so you kill two birds with one stone!

$(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)$

$(y-2)/(x-2) = (4-2)/(-1-2) = 2/-3 " this value is the slope"$

$(y-2)/(x-2) = -2/3" cross multiply"$

$3y - 6 = -2x +4$

$3y = -2x +10$

$y = (-2x)/3 +10/3$

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How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

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