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Pepsi [2]
2 years ago
9

Find the equation of the line that passes through (–3, 2) and the intersection of the lines x–2y=0 and 3x+y+5=0.

Mathematics
2 answers:
ipn [44]2 years ago
7 0

Answer:

\frac{19}{7}x+\frac{11}{7}y+5=0

Step-by-step explanation:

the intersection of x-2y=0 and 3x+y+5 is (\frac{-10}{7};\frac{-5}{7})

=> the line : \frac{19}{7}x+\frac{11}{7}y+5=0

BabaBlast [244]2 years ago
3 0

Answer:

Point \ of \ intersection = (\frac{-10}{7} , \frac{-5}{7})\\\\Equation \ of \ line : y = -\frac{19}{11}x - \frac{35}{11}

Step-by-step explanation:

<em><u>Find intersection of the given lines :</u></em>

x - 2y = 0 => x = 2y ----------- ( 1 )

3x + y = - 5 -------------------- ( 2 )

Substitute ( 1 ) in ( 2 ) :

                               3x + y = - 5

                               3 ( 2y ) + y = - 5

                                6y + y = - 5

                                  7y = - 5

                                    y = -\frac{5}{7}

Substitute y in ( 1 ) :

                            x = 2y

                           x = 2 \times \frac{-5}{7} = - \frac{10}{7}

Therefore , \ point \ of \ intersection\ is ( -\frac{10}{7}, -\frac{5}{7} )

<em><u>To find the equation of the line passing through ( - 3, 2) and point of intersection : </u></em>

Standard equation of a line : y = mx + b , where m is the slope, b is the y intercept.

So step 1 : <em><u>Find slope , m:</u></em>

 slope, m = \frac{y_2 - y_1}{x_2 - x_1}       [ \ where \ (x_1, y_ 1 ) = ( -3, 2 ) \ and \ (x_2, y_ 2 ) = ( \frac{-10}{7} , \frac{-5}{7}) \ ]

              = \frac{\frac{-5}{7}-(2)}{\frac{-10}{7} - (-3)}\\\\= \frac{-5- 14}{-10 + 21}\\\\=\frac{-19}{11}\\\\=-\frac{19}{11}

Step 2 : <em><u>Equation of the line :</u></em>

<em><u /></em>(y - y _1) = m (x - x_1)\\<em><u /></em>

<em><u /></em>(y - 2 ) = -\frac{19}{11}(x -( -3))\\\\(y - 2 ) = -\frac{19}{11} (x+ 3)\\\\y = -\frac{19}{11} (x+ 3) + 2\\\\ y = -\frac{19}{11}x +(-\frac{19}{11} \times 3) + 2\\\\y= - \frac{19}[11}x +(\frac{-57}{11} + 2)\\\\y= - \frac{19}{11}x +(\frac{-57+ 22}{11})\\\\y= - \frac{19}{11}x +(\frac{-35}{11})\\\\<em><u /></em>

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