what is the equation of the line with a slope of 1/3 passing through the point (-6,-4)

Question

the answer can either be x-3y=6, 4x+6y=-8, x-8y=3, or 10x+y=1

Answer 1

You may either: (1) determine the equation of the line in Standard Format and compare it to the possible answers, or (2) determine the slope of each of the possible answers and whether they contain the given point to determine the correct answer.  Let's do (2) [note: this is also a way of checking (1) if you have done that].  If there is only one correct answer, you have found it super-quickly.

 

The Standard Form of the equation of a line is Ax+By=C.  The slope of that line is (-A/B).

    Line                     Slope

  --------                  -------

  x-3y=6                   1/3

 4x+6y=-8               -2/3

  x-8y=3                   1/8

 10x+y=1                 -10

 

Now, if you are taking a test (especially a Standardized test), quickly move on and only come back to this question for checking.

 

If you want to check that the point (-6,-4) is on the line:

 

    Line                      (-6,-4) on line?
  --------                  -------------------
  x-3y=6                 -6+12=6 ?    yes
 4x+6y=-8               -24-24=-8     no
  x-8y=3                  -6+32=3       no
 10x+y=1                 -60-4=1       no

Answer 2

The slope-intercept form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept.

We are given the slope, m=31​, meaning that the equation so far is y=31​x+b.

To find the y-intercept (b), we can substitute the coordinates of the given point (−6,−4) into the equation.

−4=31​(−6)+b

−4=−2+b

−4+2=b

−2=b

So, the y-intercept is −2.

putting it all together then makes the equation of the line

y=31​x−2

Answer 3

You can use the point-slope form of a line.  This makes things easier.

 

y - y₁ = mx - mx₁

 

where:

m = slope

(x₁ , y₁) = (-6, -4)

 

Rewriting the formula so that it is in standard form gives you

 

-mx + y = y₁ - mx₁

 

-(1/3)x + y = -4 - (1/3)(-6)

 

-(1/3)x + y = -2

 

 

Multiply both sides of the equation by -3.

 

x - 3y = 6

Answer 4

 

The equation of the line is y = M x  +   B

 

solving for intercept B, we get  B = y - Mx

 

slope M = 1/3, (-6,-4) ---> x = -6, when y = -4

 

B = y - Mx = -4 - (1/3)(-6) = -4 - (-6/3) = -4 - (-2) = - 4 + 2= -2

 

THe equation is y = 1/3X + -2 = 1/3X - 2 = X/3 - 2 

Multiplying everything by 3 to clear the fraction:


3y = x - 6

0 = x - 6 - 3y

6 = x - 3y

x - 3y = 6