The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y plus 7 equals negative startfraction 2 over 5 endfraction left-parenthesis x minus 10 right-parenthesis.. what is the standard form of the equation for this line?

2x – 5y = –15
2x – 5y = –17
2x + 5y = –15
2x + 5y = –17

For this case we have that by definition, the standard form of a linear equation is:

 We have the following equation of the point-slope form:

We manipulate the equation algebraically to convert it to the standard form:

We apply distributive property to the terms within parentheses, taking into account that:

We subtract 4 from both sides of the equation:

We multiply by 5 on both sides of the equation:

Adding 2x to both sides of the equation:

Subtracting 15 from both sides of the equation:

Thus, the standard form of the equation is:

Option C

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