Question

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

Answer 1

Given:

There are given the graph of the line.

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where,

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

Then,

Put all the given values into the above formula

So,

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

Now,

From the formula of slop-point form:

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

Where,

$x_1=0,y_1=4,m=\frac{1}{3}$

Then,

Put all values into the above formula:

So,

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

Final answer:

Hence, the equation of the line is shown below:

$y=\frac{1}{3}x+4$