Mathematics
Grade-8
Easy

Question

The linear equation that have slope 1 third is

  1. y = 3x
  2. y = -3x
  3. 3y = x
  4. 3y = -x

Hint:

A line is a one-dimensional figure, which is consists of a set of points and it has no end points. Line is also known as the shortest distance between two points. Line can be expressed in form of an equation whose standard form is y=mx+c, where m is the slope of the line and c is the intercept of the line. Here, we have to write the equation of the line which can be done by using the slope given in the question.

The correct answer is: 3y = x


In the question the slope of a equation of line is 1 third
We have to find the equation of the line having slop 1 third.

In option a the equation is
y=3x       .............(1)
On comparing eq 1 with y=mx+c we get, m=3 and c=0.
Here, the slope of the line is 3.
In option b the equation of line is
y=-3x            ................(2)
On comparing eq 2 with y=mx+c we get, m=-3.
Here, the slope of the line is -3.
In option c the equation of line is
3y=x              ................(3)
Convert eq 3 in the form of y=mx+c.
3 y equals x
rightwards double arrow y equals 1 third x space space space space space space space space space space.............. left parenthesis 4 right parenthesis
On comparing eq 4 with y=mx+c we get, m=1 third.
Here, the slope of the line is 1 third.
In option d the equation of line is
3y=-x           ..............(5)
Convert eq 5 into the form y=mx+c.
3 y equals negative x
rightwards double arrow y equals fraction numerator negative 1 over denominator 3 end fraction x space space space space space space space space space space space space................. left parenthesis 6 right parenthesis
On comparing eq 6 with y=mx+c, we get m=fraction numerator negative 1 over denominator 3 end fraction.
Here, the slope of the line is fraction numerator negative 1 over denominator 3 end fraction.
So, the equation having slope 1 third is 3y=x.
Therefore the correct option is c, i.e., 3y=x.

The standard equation of line is y=mx+c, where m is the slope of the line and c is the intercept. To write the equation of a line we need to find the value of slope and the intercept.

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