MATH SOLVE

2 months ago

Q:
# The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?10x + 3y - 1 = 0x + 3y + 10 = 0x + 3y - 10 = 0

Accepted Solution

A:

The answer is: [B]: " x + 3y + 10 = 0 " .

______________________________________________________

Explanation:

______________________________________________________

Note the equation for a line; in 'slope-intercept form': "y = mx + b" ;

in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;

"m" = the slope of the line; and is the co-efficient of "x" ;

b = the "y-intercept"; (or the "y-coordinate of the point of the "y-intercept").

______________________________________________________

So, given the information in this very question/problem:

______________________________________________________

slope = m = (-1/3) ;

b = y-intercept = (10/3) ;

______________________________________________________

And we can write the equation of the line; in "slope-intercept form"; that is:

______________________________________________________

" y = mx + b " ; as:

______________________________________________________

" y = (-1/3)x + (10/3) " ;

______________________________________________________

Now, the problem asks for the equation of this line; in "general form"; or "standard format"; which is:

________________________________________

"Ax + By + C = 0 " ;

________________________________________

So; given:

____________________________________

" y = (-1/3)x + (10/3) " ;

____________________________________

We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;

→ 3* { y = (-1/3)x + (10/3) } ;

→ 3y = -1x + 10 ;

↔ -1x + 10 = 3y ;

Subtract "(3y)" from each side of the equation:

____________________________________

-1x + 10 − 3y = 3y − 3y ;

to get:

-1x + 10 − 3y = 0 ;

↔ -1x − 3y − 10 = 0 ;

→ This is not one of the "3 (THREE) answer choices given" ;

→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:

-1 * {-1x − 3y − 10 = 0} ;

to get:

______________________________________________________

→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."

______________________________________________________

Note that is equation is in the "standard format" ;

→ " Ax + By + C = 0 " .

______________________________________________________

______________________________________________________

Explanation:

______________________________________________________

Note the equation for a line; in 'slope-intercept form': "y = mx + b" ;

in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;

"m" = the slope of the line; and is the co-efficient of "x" ;

b = the "y-intercept"; (or the "y-coordinate of the point of the "y-intercept").

______________________________________________________

So, given the information in this very question/problem:

______________________________________________________

slope = m = (-1/3) ;

b = y-intercept = (10/3) ;

______________________________________________________

And we can write the equation of the line; in "slope-intercept form"; that is:

______________________________________________________

" y = mx + b " ; as:

______________________________________________________

" y = (-1/3)x + (10/3) " ;

______________________________________________________

Now, the problem asks for the equation of this line; in "general form"; or "standard format"; which is:

________________________________________

"Ax + By + C = 0 " ;

________________________________________

So; given:

____________________________________

" y = (-1/3)x + (10/3) " ;

____________________________________

We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;

→ 3* { y = (-1/3)x + (10/3) } ;

→ 3y = -1x + 10 ;

↔ -1x + 10 = 3y ;

Subtract "(3y)" from each side of the equation:

____________________________________

-1x + 10 − 3y = 3y − 3y ;

to get:

-1x + 10 − 3y = 0 ;

↔ -1x − 3y − 10 = 0 ;

→ This is not one of the "3 (THREE) answer choices given" ;

→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:

-1 * {-1x − 3y − 10 = 0} ;

to get:

______________________________________________________

→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."

______________________________________________________

Note that is equation is in the "standard format" ;

→ " Ax + By + C = 0 " .

______________________________________________________