Question

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 ?

Answer 1

Linear Equations

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

`Ax+By=C`

• A, B and C are typically integers

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

`y-y_1=m(x-x_1)`

• m is the slope
• 
  `(x_1,y_1)` 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
  `y+7=-(5)/(2)(x-10)`

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.

`y+7=-(5)/(2)(x-10)`

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

`2y+14=-5(x-10)`

⇒ Now, open up the parentheses:

`2y+14=-5x+50`

⇒ Move -5x to the other side:

`5x+2y+14=50`

⇒ Move 14 to the other side:

`5x+2y=50-14`

⇒ Combine like terms:

`5x+2y=36`

Answer

`5x+2y=36`