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What is the equation of a line that is parallel to 2x+5y=10 and passes through the point (5, -4)?

Enter your answer in slope-intercept form (y=mx+b) in the box

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Dirtyfacebabyaj

Answer: The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2

Step-by-step explanation: The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line 2x + 5y = 10 is:

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 10

Hence the slope of the line 2x + 5y = 10 is -2/5

Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
  • 2x+5y=10

Isolate y

[tex]\\ \sf\longmapsto 5y=-2x+10[/tex]

[tex]\\ \sf\longmapsto y=-2/5x+2[/tex]

  • m=-2/5

Parallel line has equal slope

Equation of line in point slope form

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

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

[tex]\\ \sf\longmapsto 5y+20=-2x+10[/tex]

[tex]\\ \sf\longmapsto 2x+5y+10=0[/tex]

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