Question

Which Linear Equation Is Shown In The Graph Below

Answer 1

x+2y= -4

Explanation:

The standard form of any linear function is

y = mx + c

where y is the y-coordinate at a point

x is the x coordinate at a point

m is the gradient/slope of the linear function

c is any number that is an element of real numbers

To find the equation of the linear function, you have to first determine the gradient of the linear function(m)

The formula for calculating the gradient is

`m = (ya - yb)/(xa - xb)`

Choose any two point on the linear function to substitute in the places of x and y

FOR EXAMPLE

I will use the (-2;-1) as my a and (4;-4) as my b

`(( - 1) - ( - 4))/( ( - 2) - (4))`

`= ( - 1)/(2)`

The new equation will now be

`y = ( - 1)/(2) x + c`

To find c

Choose any coordinates

Substitute the x any y values of the coordinates in the new equation.

`( - 4) = ( - 1)/(2) (4) + c \\ \: - 4 = - 2 + c \\ - 4 + 2 = c \\ - 2 = c`

The complete equation will now be

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

Multiply every term by -2 to get rid of the fraction and make x to have a coefficient of 1.

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

`- 2y = x + 4`

From -2y=x+4

x+2y=-4

Answer 2

option 4

Explanation:

1st point: (0,-2)

2nd point: (4,-4)

m= rise/run

= -2-(-4)/0-4

= 2/-4

= -1/2

y= mx+c

c (y-intercept)= -2

y= -1/2x-2

2y= -x-4

x+2y= -4