Question

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

Answer 1

2x + 5y = -15 is the standard form of equation

Solution:

Given that,

The point slope form of the equation of the line that passes through (-5, -1) and (10, -7) is given by:

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

We have to write the standard form of the equation

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

Let us convert the given equation into standard form

`y + 7 = (-2)/(5)(x-10)\\\\\text{Simplify the right hand side of equation }\\\\y + 7 = (-2x)/(5)+(20)/(5)\\\\y + 7 = (-2x +20)/(5)\\\\5(y+7) = -2x + 20\\\\\text{Simplify the left hand side of equation }\\\\5y + 35 = -2x + 20\\\\\text{Move the variables to left side of equation and constants to right side }\\\\2x + 5y = 20 - 35\\\\2x + 5y = -15`

Thus the standard form of equation is found