Question

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

2x – 5y = –15


2x – 5y = –17


2x + 5y = –15


2x + 5y = –17

Answer 1

Answer: The correct option is (C)
`2x+5y=-15.`

Step-by-step explanation: Given that the equation of the line that passes through (-5, -1) and (10, -7) in point-slope form is given by

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

We are to find the standard form of the equation for the above line.

We know that the STANDARD form of the equation of a line is given by

`ax+by=c,~~~~~\textup{[a and b cannot be zero at the same time]}.`

From equation (i), we have

`y+7=-(2)/(5)(x-10)\\\\\Rightarrow 5(y+7)=-2(x-10)\\\\\Rightarrow 5y+35=-2x+20\\\\\Rightarrow 2x+5y=20-35\\\\\Rightarrow 2x+5y=-15.`

Thus, the required standard form is
`2x+5y=-15.`

Option (C) is CORRECT.