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Write an equation parallel to x-4y=20 that passes through the point 2,-5

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mhanifa

Answer:

  • x - 4y = 22

Step-by-step explanation:

Given line:

  • x - 4y = 20

Convert the equation into slope-intercept form:

  • x - 4y = 20
  • 4y = x - 20
  • y = 1/4x - 5

It has a slope of 1/4.

Parallel lines have equal slopes.

Find the parallel line lines that passes through the point (2, - 5):

  • y = 1/4x + b

Substitute x and y values to work out the value of b:

  • - 5 = 1/4*2 + b
  • - 5 = 1/2 + b
  • b = - 5 - 1/2
  • b = - 11/2

The line is:

  • y = 1/4x - 11/2

Covert this into standard form:

  • y = 1/4x - 11/2
  • 4y = x - 22
  • x - 4y = 22
Ver imagen mhanifa
  • x-4y=20

Isolate y

[tex]\\ \sf\longmapsto x-20=4y[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{1}{4}x-5[/tex]

  • m=1/4
  • Parallel lines have equal slope

Equation of line in point slope form

[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\\ \sf\longmapsto y+5=1/4(x-2)[/tex]

[tex]\\ \sf\longmapsto 4y+20=x-2[/tex]

[tex]\\ \sf\longmapsto x-4y+22=0[/tex]

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