Question

Hello this is what im.stuck on and need help ty

Answer 1

Given:

There are given the graph of the line.

Step-by-step explanation:

To write the equation of the line, first, we need to select two points from the graph:

So,

The points is:

`(0,4),(6,6)`

Now,

For the equation, first, find the slope of the line from the given points:

So,

Fro the formula to find the slope:

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`x_1=0,y_1=4,x_2=6,y_2=6`

Then,

Put all the given values into the above formula

So,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=\frac{6_{}-4_{}}{6_{}-0} \\ m=(2)/(6) \\ m=(1)/(3) \end{gathered}`

Now,

From the formula of slop-point form:

`y-y_1=m(x-x_1)`

Where,

`x_1=0,y_1=4,m=(1)/(3)`

Then,

Put all values into the above formula:

So,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-4_{}=(1)/(3)(x-0) \\ y-4=(1)/(3)x \\ 3y-12=x \\ 3y-12-x=0 \\ 3y-x-12=0 \\ 3y=x+12 \\ y=(1)/(3)x+4 \end{gathered}`

Final answer:

Hence, the equation of the line is shown below:

`y=(1)/(3)x+4`