How do i write this linear equation?

Question

x-intercept is -2. and goes through the point (1,1)

Answer 1

x - intercept is - 2 means  x= - 2 when y = 0

that is  0 = -2m + c

        => c = 2m

The line passes through (1,1)

i.e 1 = m*1 + c

=> 1 = m + 2m

=> m = 1/3

c= 2/3

So equation is y = 1/3 x + 2/3

Answer 2

Generally a linear equation is

             y=mx +c

For the x-intercept the value of y=0

             0=-2m +c

Using the point (1,1)

             1=m +c

These are simultaneous equations

             -2m + c=0

               m + c =1

                    -3m=-1

                        m=1/3

Substituting m=1/3 into m + c =1 we get

                   c=2/3

Linear equation now is y=1/3x +2/3

Answer 3

Equation used: y=mx+c

When x-intercept is -2 it basically means (-2,0)

Now we have 2 points.

To find m,

(y1-y2)/(x1-x2)=(1-0)/(1-(-2))= 1/3

To find c,

Plug in either one of the given points into the equation.

y=1/3*x+c

Using point (1,1)

1=1/3*1+c

c=2/3

Plug into the linear equation, you'll get:

y = 1/3*x + 2/3

or

3y=x+2

  

Answer 4

(-2,0) and (1,1) are both points. y=mx+b

m = y(1)-y(2)/x(1)-x(2)

=1-0/1-(-2)

=1/3

y=mx+b

1=1/3(1)+b

1-(1/3)=b

2/3=b

y=1/3x+2/3

Another way to do it if you're allowed is to use the standard formula and go (y-y(0))=m(x-x(0)). But that's kind of cheating in this case. Haha.

Answer 5

X intercept is such a point where y=0

therefore the coordinate of x-intercept is    (-2,0)

Now we will find the slope between two points

m = (0-1)/(-2-1)

m= 1/3

Now assuming another point on the same line to be (x,y)

and the other point to be (1,1)

Being Linear equation the slope will remain same so

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

solving it will result in

y = x/3 + 2/3