How do you graph the inequality #3x-4y

Question

How do you graph the inequality #3x-4y<= 16#?

Avery Alexander · Accepted Answer

Draw the straight line #3x-4y=16#. Including the line shade the region above this lin, in the positive y-direction Enter therein #3x-4y<=16# Rearranging, #y>=(3/4)x-4#. Draw the straight line #y=(3/4)x-4#.. On this line and above, in the positive y-direction, #y>=(3/4)x-4#, and so, #3x-4y<=16#.

Genesis Allen · Answer

undefined To graph the inequality $3x - 4y \leq 16$:

1. First, rearrange the inequality into slope-intercept form, $y \leq mx + b$, where $m$ is the slope and $b$ is the y-intercept.
2. Solve for $y$ to get $y \geq \frac{3}{4}x - 4$.
3. Plot the y-intercept at $-4$ on the y-axis.
4. Use the slope $\frac{3}{4}$ to find another point. Since the slope is positive, move up 3 units and to the right 4 units from the y-intercept and plot another point.
5. Draw a solid line through these points to represent the boundary of the inequality. Since the inequality is inclusive (i.e., $\leq$), use a solid line. If it were strictly less than (<), you would use a dashed line.
6. Shade the area below the line to represent all the points that satisfy the inequality. Since $y$ is less than or equal to the expression, shade below the line.

HIX Tutor · Answer

undefined To graph the inequality 3x - 4y ≤ 16, follow these steps:

1. **Change to Equation**: Start by changing the inequality to an equation:  
   $3x - 4y = 16$.

2. **Find Intercepts**:
   - **X-Intercept**: Set $y = 0$:  
     $3x = 16$  
     $x = \frac{16}{3} \approx 5.33$  
     So, the point is $(5.33, 0)$.
   - **Y-Intercept**: Set $x = 0$:  
     $-4y = 16$  
     $y = -4$  
     So, the point is $(0, -4)$.

3. **Plot Points**: On graph paper, plot the points $(5.33, 0)$ and $(0, -4)$.

4. **Draw the Line**: Draw a straight line through these points. **Since the inequality is ≤, use a solid line.** This shows points on the line are included.

5. **Shade**: Choose a test point not on the line, like $(0, 0)$.  
   Substitute into the original inequality:  
   $3(0) - 4(0) ≤ 16$  
   $0 ≤ 16$ (True).  
   Shade the area that includes $(0, 0)$.

Now your graph has the line and the shaded area showing the solution!

How do you graph the inequality #3x-4y&lt;= 16#?

How do you graph the inequality #3x-4y<= 16#?