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HELP NOW Choose all that give the correct equation of the line parallel or perpendicular to the given line passing through the point. The line y = 7 5 x + 4 passing through the point (5, 2) is parallel to the line y = 7 5 x βˆ’ 5. The line βˆ’x + y = βˆ’1 passing through the point (1, βˆ’5) is perpendicular to the line y = βˆ’x βˆ’ 4. The line y = 9 2 x βˆ’ 5 passing through the point (3, 4) is perpendicular to the line y = 9 2 x βˆ’ 19 2 . The line 3x + 7y = 0 passing through the point (βˆ’3, βˆ’5) is parallel to the line y = 7 3 x + 2.

Respuesta :

Answer:

Neither of the options are correct.

Step-by-step explanation:

Option A :

Line parallel to the equation [tex]y = \frac{7}{5}x - 5[/tex] will have equation

[tex]y = \frac{7}{5}x + c[/tex] ........... (1)

If it passes through the point (5,2) then this will satisfy the equation (1).

Hence, [tex]2 = \frac{7}{5} \times 5 + c[/tex]

β‡’ c = - 5

So, the equation (1) becomes [tex]y = \frac{7}{5}x - 5[/tex] (Answer)

Option B :

Line perpendicular to the equation y = - x - 4 will have equation - x + y = c ........... (2)

{Because slope of the original line is - 1 and that of the perpendicular line is 1 and hence the product is (- 1) Γ— (1) = - 1}

Now, if the equation (2) passes through the point (1,-5), then we get,

- 1 + (- 5) = c

β‡’ c = - 6

Therefore, the equation (2) becomes, -x + y = - 6. (Answer)

Option C :

Line perpendicular to the equation [tex]y = \frac{9}{2} x - \frac{19}{2}[/tex] will have equation [tex]y = - \frac{2}{9}x + c[/tex] ........... (3)

{Because slope of the original line is [tex]\frac{9}{2}[/tex] and that of the perpendicular line is [tex]- \frac{2}{9}[/tex] and hence the product is ([tex]\frac{9}{2}[/tex]) Γ— ([tex]- \frac{2}{9}[/tex]) = - 1}

Now, if the equation (3) passes through the point (3,4), then we get,

[tex]4 = - \frac{2}{9}\times 3 + c[/tex]

β‡’ [tex]c = \frac{14}{3}[/tex]

Therefore, the equation (3) becomes, [tex]y = - \frac{2}{9}x + Β \frac{14}{3}[/tex]. (Answer)

Option D :

Line parallel to the equation [tex]y = \frac{7}{3}x + 2[/tex] will have equation

[tex]y = \frac{7}{3}x + c[/tex] ........... (4)

If it passes through the point (-3,-5) then this will satisfy the equation (1).

Hence, [tex]- 5 = \frac{7}{3} \times (-3) + c[/tex]

β‡’ c = 2

So, the equation (1) becomes [tex]y = \frac{7}{3}x + 2[/tex] (Answer)

Therefore, neither of the options are correct. (Answer)

Answer:

A and B

Step-by-step explanation:

ο»ΏThe line y = Β 7/5 x + 4 passing through the point (5, 2) is parallel to the line y = Β 7 /5x βˆ’ 5.

and

The line βˆ’x + y = βˆ’1 passing through the point (1, βˆ’5) is perpendicular to the line y = βˆ’x βˆ’ 4.

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