Question

First blank options: does not change or change 2nd blank options: a constant, a decreasing, or an increasing 3rd blank options: can or cannot 4th blank options: is or is not PLEASE do 27 also

Answer 1

As given by the question

There are given that the graph.

Now,

For finding the linear function, first choose two points from the graph.

Then,

The point is:

$(1,\text{ 1) and (2, 2)}$

Then,

Find the slope of the given line:

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

Then,

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

Now,

From the equation of the two-point form:

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

Then,

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

hence, the correct answer is yes, the given function is linear.