How do you graph #9y

Question

How do you graph #9y<=12x#?

Eva Adamson · Accepted Answer

To graph an inequality, try to manipulate it into the form #y \le f(x)# (or #y \ge f(x)#). Once this is done, the points which solve the inequality will be those under (or above) the graph of the function: in fact, #y=f(x)# are exactly the points of the graph. This means that #y \le f(x)# represents all the point below the graph, and vice versa #y \ge f(x)# represents all the point above the graph. In this case, you only need to divide by 9 both sides to get
#y \le 12/9 x# which is equivalent to #y \le 4/3 x#. So, you only need to draw the #y=4/3 x# line, and take all the part of the plan below the line. Drawing such a line is quite easy, since it crosses the origin (you can see that #(0,0)# fits in the equation, as #0=4/3*0#), and a second point, chosen as you want. For example, if #x=3# you get #y=4#. So, the line passes through the two points #(0,0# and #(3,4)#, and any line is completely determined by two of its point. Take a look at the graph: graph{9y\le 12x [-10, 10, -5, 5]}

Eli Assouline · Answer

undefined To graph the inequality $9y \leq 12x$, follow these steps:

1. Start by graphing the line $9y = 12x$ by finding two points on the line. Let's choose $x = 0$ and $x = 4$ for convenience.

- When $x = 0$, $9y = 12 \cdot 0$ gives $y = 0$. So, one point is (0, 0).
   - When $x = 4$, $9y = 12 \cdot 4$ gives $y = \frac{16}{3}$. So, another point is (4, $ \frac{16}{3} $).

2. Plot these two points on a coordinate plane and draw a dashed line through them since the inequality is $9y \leq 12x$, not $9y < 12x$.

3. Finally, shade the region below the line since it represents all the points where $9y$ is less than or equal to $12x$.

The graph should include the line $9y = 12x$ passing through (0, 0) and (4, $ \frac{16}{3} $), and the shaded area below the line.

How do you graph #9y&lt;=12x#?

How do you graph #9y<=12x#?