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8. Write the equation of the line that is parallel to the line 2x + 5y = 15 and passes through the
point (-10, 1).

Sagot :

Fieryanswererftidn

Answer:

[tex]\sf y = \bold -\frac{2}{5} x -3[/tex]

Explanation:

part A identification for slope:

[tex]\sf 2x + 5y = 15[/tex]

[tex]\sf 5y = -2x + 15[/tex]

[tex]\sf y = \frac{-2x + 15}{5}[/tex]

[tex]\sf y = -\frac{2 }{5} x+3[/tex]

comparing with slope intercept form: y = mx + b

we can find that here the slope is [tex]\bold -\frac{2}{5}[/tex]

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

y - y₁ = m( x - x₁ )

[tex]\sf y - 1 = \bold -\frac{2}{5} (x --10)[/tex]

[tex]\sf y = \bold -\frac{2}{5} x -4 + 1[/tex]

[tex]\sf y = \bold -\frac{2}{5} x -3[/tex]

Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

View image Fieryanswererft

Solution:

Step-1: Convert the line into slope intercept form.

  • 2x + 5y = 15
  • => 5y = -2x + 15
  • => y = -0.4x + 3

Step-2: Use the point slope form formula.

  • y - y₁ = m(x - x₁)
  • => y - 1 = -0.4{x - (-10)}
  • => y - 1 = -0.4{x + 10}
  • => y - 1 = -0.4x - 4
  • => y = -0.4x - 3
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