Which graph represents $$4 x+7 y \leq-21$$ ?


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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Which graph represents $$4 x+7 y \leq-21$$ ?
</textarea>Which graph represents <math><semantics><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>≤</mo><mo>−</mo><mn>2</mn><mn>1</mn></mrow><annotation encoding="application/x-tex">4 x+7 y \leq-21</annotation></semantics></math>4x+7y≤−21 ?
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>here,converting inequality to equality, $$4x+7y=-21$$

or, $$\frac{4x}{-21}+\frac{7y}{-21}=1$$

or, $$\frac{x}{-5.25}+\frac{y}{-3}=1$$

Therefore , x-intercept= $$(-5.25,0)$$ and y -intercept= $$(0,-3)$$

Putting $$(0,0)$$ in $$4 x+7 y \leq-21,$$ but $$ \quad 0 \nless-21$$
So, the solution region does not contain origin.

Now solid line will be there.Since, it is less than and equal to problem.

![](http://admin.getprephub.com/media/editor/eq13_20221114210541554669.png)</textarea>here,converting inequality to equality, <math><semantics><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>=</mo><mo>−</mo><mn>2</mn><mn>1</mn></mrow><annotation encoding="application/x-tex">4x+7y=-21</annotation></semantics></math>4x+7y=−21
or, <math><semantics><mrow><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mrow><mo>−</mo><mn>2</mn><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>7</mn><mi>y</mi></mrow><mrow><mo>−</mo><mn>2</mn><mn>1</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\frac{4x}{-21}+\frac{7y}{-21}=1</annotation></semantics></math>​−21​​4x​​+​−21​​7y​​=1
or, <math><semantics><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mo>−</mo><mn>5</mn><mi mathvariant="normal">.</mi><mn>2</mn><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>y</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\frac{x}{-5.25}+\frac{y}{-3}=1</annotation></semantics></math>​−5.25​​x​​+​−3​​y​​=1
Therefore , x-intercept= <math><semantics><mrow><mo>(</mo><mo>−</mo><mn>5</mn><mi mathvariant="normal">.</mi><mn>2</mn><mn>5</mn><mo separator="true">,</mo><mn>0</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(-5.25,0)</annotation></semantics></math>(−5.25,0) and y -intercept= <math><semantics><mrow><mo>(</mo><mn>0</mn><mo separator="true">,</mo><mo>−</mo><mn>3</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(0,-3)</annotation></semantics></math>(0,−3)
Putting <math><semantics><mrow><mo>(</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(0,0)</annotation></semantics></math>(0,0) in <math><semantics><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>≤</mo><mo>−</mo><mn>2</mn><mn>1</mn><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">4 x+7 y \leq-21,</annotation></semantics></math>4x+7y≤−21, but <math><semantics><mrow><mspace width="1em"></mspace><mn>0</mn><mo>≮</mo><mo>−</mo><mn>2</mn><mn>1</mn></mrow><annotation encoding="application/x-tex"> \quad 0 \nless-21</annotation></semantics></math>0≮−21 So, the solution region does not contain origin.
Now solid line will be there.Since, it is less than and equal to problem.
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