How do you write an equation of a line given (-1, 2) and (3, -4)?

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How do you write an equation of a line given (-1, 2) and (3, -4)?

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Answer 1 · 2017-10-17T03:23:20

$3 x + 2 y + 1 = 0$ $3x+2y+1=0$

Explanation:

Standard form of equation with two points given is
$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$ $(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$
$\frac{y - (- 4)}{2 - (- 4)} = \frac{x - 3}{- 1 - 3}$ $(y-(-4))/(2-(-4))=(x-3)/(-1-3)$

$\frac{y + 4}{6} = \frac{x - 3}{- 4}$ $(y+4)/6=(x-3)/(-4)$
$- 4 y - 16 = 6 x - 18$ $-4y-16= 6x - 18$

$6 x + 4 y = 2$ $6x+4y=2$
$3 x + 2 y = 1$ $3x+2y=1$

Answer 2 · 2017-10-17T03:43:02

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

Explanation:

Okay so there are 3 main forms you can use:
- slope-intercept form [ $y = m x + b$ $y=mx+b$ ]
- standard form [ $A x + B y = C$ $Ax+By=C$ ]
- point-slope form [ $y_{1} - y_{2} = m (x_{1} - x_{2})$ $y_1-y_2=m(x_1-x_2)$ ]

Since you did not specify which form you wanted it in, I am going to use slope-intercept form because that's the easiest to understand, in my opinion. (:

$y = m x + b$ $y=mx+b$

SLOPE ( $m$ $m$ )
To find $m$ $m$ (slope), you need to find $\frac{r i s e}{r u n}$ $(rise)/(run)$ , or which is the change in $y$ $y$ divided by the change in $x$ $x$ . Use this formula: $\frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ $(y_1-y_2)/(x_1-x_2)$
$(- 1, 2) = (x_{1}, y_{1})$ $(-1, 2) = (x_1, y_1)$
$(3, - 4) = (x_{2}, y_{2})$ $(3, -4) = (x_2, y_2)$

It doesn't matter which coordinate pair you choose to be $(x_{1}, y_{1})$ $(x_1, y_1)$ or $(x_{2}, y_{2})$ $(x_2, y_2)$ . Just stay consistent!

$m = \frac{2 - (- 4)}{- 1 - 3} = \frac{2 + 4}{- 1 - 3} = \frac{6}{- 4} = - \frac{3}{2}$ $m = [2-(-4)]/[-1-3] = (2+4)/(-1-3) = 6/-4 = -3/2$
$m$ $m$ = -3/2#

Y-INTERCEPT ( $b$ $b$ )
Choose one of the coordinates to substitute into $y = m x + b$ $y=mx+b$ , which will be substituting for $x$ $x$ and $y$ $y$ .
I chose $(- 1, 2)$ $(-1, 2)$ . Substitute $m$ $m$ for $- \frac{3}{2}$ $-3/2$ .
$(2) = (- \frac{3}{2}) (- 1) + b$ $(2)=(-3/2)(-1)+b$
Solve for $b$ $b$ .
$2 = \frac{3}{2} + b$ $2=3/2+b$
$b = \frac{1}{2}$ $b=1/2$

FINAL FORM
Substitute $m$ $m$ and $b$ $b$ for their values. This is your answer!
$y = - \frac{3}{2} x + \frac{1}{2}$ $y=-3/2x+1/2$

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How do you write an equation of a line given (-1, 2) and (3, -4)?

2 Answers

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