Question

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

Answer 1

• x-4y=20

Isolate y

`\\ \sf\longmapsto x-20=4y`

`\\ \sf\longmapsto y=(1)/(4)x-5`

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

Equation of line in point slope form

`\\ \sf\longmapsto y-y_1=m(x-x_1)`

`\\ \sf\longmapsto y+5=1/4(x-2)`

`\\ \sf\longmapsto 4y+20=x-2`

`\\ \sf\longmapsto x-4y+22=0`

Answer 2

• x - 4y = 22

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