Question

Find the inequality represented by the graph

Answer 1

Answer:

$y\leq -\frac{1}{3}x+1$

Step-by-step explanation:

Given:

From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.

Now, for a line with two points $(x_1,y_1)\ and\ (x_2,y_2)$, the slope is given as:

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

Here, $(x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)$. Therefore,

$m=\frac{1-0}{0-3}=-\frac{1}{3}$

Now, y-intercept is $b=1$

Therefore, the standard form of a line is of the form: $y=mx+b$. So, the equation of the line on the graph is:

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

Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,

$y\leq -\frac{1}{3}x+1$