What is the equation of the line that passes through (6,11) ,( - 1,2)?

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Answer 1 · 2017-12-12T05:28:01

$y = \frac{9}{7} x + \frac{23}{7}$ $color(blue)(y=9/7x+23/7)$

We are given two points : -

$(6, 11), (- 1, 2)$ $color(red)((6, 11), (-1, 2)$ .... Points

Let, $x_{1} = 6 and y_{1} = 11$ $color(green)(x_1 = 6 and y_1 = 11)$

Let, $x_{2} = - 1 and y_{2} = 2$ $color(green)(x_2 = -1 and y_2 = 2)$

Hence, the two points given to us can be written as

$(x_{1}, y_{1}), (x_{2}, y_{2})$ $color(red)((x_1, y_1), (x_2, y_2)$ .... Points

We will next find the Slope using the formula:

$S l o p e (m) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $color(green)(Slope(m) = (y_2 - y_1)/(x_2-x_1))$

$\Rightarrow S l o p e (m) = \frac{2 - 11}{- 1 - - 6}$ $rArr Slope(m) = ( 2- 11)/(-1--6)$

$\Rightarrow \frac{- 9}{- 7} = \frac{9}{7}$ $rArr (-9)/(-7) = 9/7$

Therefore,

$S l o p e (m) = \frac{9}{7}$ $Slope(m) = 9/7$

The Point-Slope Equation of a Straight Line is given by:-

$(y - y_{1}) = m (x - x_{1})$ $color(green)((y - y_1) = m(x-x_1))$ Formula.1

We can substitute the value of $S l o p e (m) = \frac{9}{7}$ $Slope(m) = 9/7$ in the equation above.

We also need a Point.

We will choose one the points given to us: $(6, 11)$ $(6, 11)$

This point $(6, 11)$ $(6, 11)$ is our $(x_{1}, y_{1})$ $(x_1, y_1)$ .

We are ready to use the Point-Slope Equation of a Straight Line using Formula.1

Substitute the values of $m$ $m$ and $(x_{1}, y_{1})$ $(x_1, y_1)$ .

$y - 11 = \frac{9}{7} (x - 6)$ $y-11 = 9/7(x-6)$

$\Rightarrow y - 11 = \frac{9}{7} x - \frac{54}{7}$ $rArr y - 11 = 9/7x-54/7$

$\Rightarrow y = \frac{9}{7} x + \frac{23}{7}$ $rArr y = 9/7x + 23/7$

Hence, the Equation of a Straight Line passing through the points $(6, 11), (- 1, 2)$ $color(red)((6, 11), (-1, 2)$ is given by:-

$y = \frac{9}{7} x + \frac{23}{7}$ $color(blue)(y = 9/7x + 23/7)$

Graph below has the equation of the straight line we found:

enter image source here