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What is the equation in point-slope form for the line parallel to y=5x-4 that contains p(-6,1)

Sagot :

VectorFundament120

Answer:

[tex]\displaystyle{y-1=5(x+6)}[/tex]

Step-by-step explanation:

A point-slope form is written in the equation of  [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]

Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:

[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)

Hi1315

Answer:

y - 1 = 5 ( x + 6 )

Step-by-step explanation:

  • We know that when two lines are parallel the slope of both lines is equal.
  • The formula that we use to find an equation of a line is y = m x + c

       Here,

          m ⇒ slope

  • Now let us take a look at the given equation which is already drawn.

    y = 5x - 4 ← equation of the old line

         Now it is clear to us that,

         m ⇒ slope of the line ⇒ 5

         c  ⇒ y-intercept ⇒ -4

  • Therefore, the slope of the new line also will be 5.

                 That is, m = 5

  • The question asked us to write the equation in point-slope form.
  • The formula to write the equation in the line in point-slope form is :

                   y - y₁ = m ( x - x₁ ).

  • Here,

        m = slope

  • Also, we can use the given coordinates to write the equation in point-slope form

           ( -6 , 1 ) ⇔ ( x₁ , y₁ )

  • So, to find the equation of the new line we can replace m, y₁ & x₁ with 5, 1 & -6 respectively.

        Let us solve this now

         y - y₁ = m ( x - x₁ )

         y - 1 = 5 ( x - ( -6) )

         y - 1 = 5 ( x + 6 )

  •   And now let us write the equation of the new line in point - slope form.

                y - 1 = 5 ( x + 6 )

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