contestada


The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is y+7= -5/2(x-10)What
is the standard form of the equation for this line ?

Respuesta :

theleangreenbean

Linear Equations

One way we can organize a linear equation is in standard form:

[tex]Ax+By=C[/tex]

  • A, B and C are typically integers

Another way we can organize a linear equation is in point-slope form:

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

  • m is the slope
  • [tex](x_1,y_1)[/tex] is a point that falls on the line

Solving the Question

We're given:

  • Line passes through (-5,-1) and (10,-7)
  • Point-slope form is [tex]y+7=-\dfrac{5}{2}(x-10)[/tex]

We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.

[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]

⇒ First, multiply both sides by 2 to get rid of the fraction:

[tex]2y+14=-5(x-10)[/tex]

⇒ Now, open up the parentheses:

[tex]2y+14=-5x+50[/tex]

⇒ Move -5x to the other side:

[tex]5x+2y+14=50[/tex]

⇒ Move 14 to the other side:

[tex]5x+2y=50-14[/tex]

⇒ Combine like terms:

[tex]5x+2y=36[/tex]

Answer

[tex]5x+2y=36[/tex]

Otras preguntas