How do you write an equation of a line given (3, 5) and (-6, -1)?

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How do you write an equation of a line given (3, 5) and (-6, -1)?

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Answer 1 · 2017-08-14T07:50:12

Find the gradient and the $y$ $y$ -intercept in $y = m x + c$ $y = mx + c$ to get

$3 y = 2 x + 9$ $3y = 2x + 9$

Explanation:

$y = m x + c$ $y=mx+c$ is the slope-intercept equation of any straight line. So we need to find $m$ $m$ , the gradient of the line, and $c$ $c$ , the $y$ $y$ -intercept.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = ( y_2 - y_1 ) / ( x_2 - x_1 )$

$y_{2}$ $y_2$ being the second $y$ $y$ value, which is $- 1$ $-1$ , and $y_{1}$ $y_1$ is $5$ $5$ . The same goes for $x_{2}$ $x_2$ and $x_{1}$ $x_1$ , so

$m = \frac{- 1 - 5}{- 6 - 3}$ $m = ( -1 - 5 ) / (-6-3)$

$m = \frac{- 6}{- 9} = \frac{2}{3}$ $m = (-6)/-9 = 2/3$

Since

$y = m x + c$ $y = mx+c$

to find $c$ $c$ do

$c = y - m x$ $c = y - mx$

We substitute one of the coordinates, for eg. $(3, 5)$ $( 3 , 5 )$ , so

$c = 5 - (\frac{2}{3}) \cdot 3$ $c = 5 - (2/3)*3$

$c = 3$ $c = 3$

Therefore, we substitute the values of $m$ $m$ and $c$ $c$ in $y = m x + c$ $y = mx + c$
to get

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

$3 y = 2 x + 9$ $3y = 2x + 9$

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How do you write an equation of a line given (3, 5) and (-6, -1)?

1 Answer

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