Questions: Match the graph a. y < -3 with its inequality. b. x ≥ 2 c. 5x + 10y > 0 d. y < x e. 2y - x ≤ 6 f. 6x + 3y > 9 g. 3y - 4x ≥ 12 h. y ≤ -2x - 4 i. 8x - 6y < 10 j. 3x - 1 ≥ y

Transcript text: Match the graph a. $y<-3$ with its inequality. b. $x \geq 2$ c. $5 x+10 y>0$ d. $y9$ g. $3 y-4 x \geq 12$ h. $y \leq-2 x-4$ i. $8 x-6 y<10$ j. $3 x-1 \geq y$

Solution

Solution Steps

To match the given inequalities with their corresponding graphs, we need to understand the nature of each inequality and how it would be represented on a coordinate plane. We will plot each inequality and visually inspect the graph to determine the correct match.

Step 1: Define the Range for $ x $ and $ y $

We define the range for $ x $ and $ y $ from -10 to 10 with 400 points in between. This gives us a grid to plot the inequalities.

Step 2: Define the Inequalities

We define the inequalities as follows:

$ a: y < -3 $
$ b: x \geq 2 $
$ c: 5x + 10y > 0 $
$ d: y < x $
$ e: 2y - x \leq 6 $
$ f: 6x + 3y > 9 $
$ g: 3y - 4x \geq 12 $
$ h: y \leq -2x - 4 $
$ i: 8x - 6y < 10 $
$ j: 3x - 1 \geq y $

Step 3: Plot Each Inequality

We plot each inequality on a coordinate plane to visually inspect and match them with their corresponding graphs.

Final Answer

Based on the visual inspection of the plots, the matches for the inequalities are as follows:

$ a: y < -3 $
$ b: x \geq 2 $
$ c: 5x + 10y > 0 $
$ d: y < x $
$ e: 2y - x \leq 6 $
$ f: 6x + 3y > 9 $
$ g: 3y - 4x \geq 12 $
$ h: y \leq -2x - 4 $
$ i: 8x - 6y < 10 $
$ j: 3x - 1 \geq y $

\[ \boxed{ \begin{aligned} &\text{a: } y < -3 \\ &\text{b: } x \geq 2 \\ &\text{c: } 5x + 10y > 0 \\ &\text{d: } y < x \\ &\text{e: } 2y - x \leq 6 \\ &\text{f: } 6x + 3y > 9 \\ &\text{g: } 3y - 4x \geq 12 \\ &\text{h: } y \leq -2x - 4 \\ &\text{i: } 8x - 6y < 10 \\ &\text{j: } 3x - 1 \geq y \\ \end{aligned} } \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!