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3 years ago

How do you graph x - y < 4

Mathematics

2 answers:

katrin [286]3 years ago

8 0

Answer: y > -4 + x

Step-by-step explanation: graph the inequality by finding the boundary line

shutvik [7]3 years ago

8 0

Answer:

y > -4 + x

***(see graph below)****

Step-by-step explanation:

Graph

x − y < 4

Solve for y

Subtract x from both sides of the inequality.

−y < 4 − x

Multiply each term in −y < 4 − x by −1

Multiply each term in −y < 4 − x by −1. When multiplying or dividing both sides of an

inequality by a negative value, f lip the direction of the inequality sign.

(−y) ⋅ −1 > 4 ⋅ −1 + (−x) ⋅ −1

Multiply (−y) ⋅ −1.

Multiply −1 by −1.

1y > 4 ⋅ −1 + (−x) ⋅ −1

Multiply y by 1.

y > 4 ⋅ −1 + (−x) ⋅ −1

Simplify each term.

Multiply 4 by −1.

y > −4 + (−x) ⋅ −1

Multiply (−x) ⋅ −1.

y > −4 + x

Find the slope and the y-intercept for the boundary line.

Rewrite in s lope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Reorder −4 and x. y > x − 4

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y = mx + b. m = 1

b = −4

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 1

intercept: (0, −4)

Graph a dashed line, then shade the area above the boundary line since y is greater than −4 + x. y > −4 + x

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Answer:Answer is option C : [ $x^{2}$ + 3x + 3 ] =0

Note: None of options matches with given question.

instead of "-3" , there should be "- $\frac{3}{2}$ ".

Step-by-step explanation:

Note: None of options matches with given question.

instead of "-3" , there should be " $\frac{3}{2}$ ".

Here, First thing you have to observe the nature of roots.

∴ x = - $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i and x = - $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$

∴ [ x+( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) ][ x+( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + x( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i)+ x( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + $\frac{3}{2}$ x + $\frac{\sqrt{3}}{2}$ ix + $\frac{3}{2}$ x - $\frac{\sqrt{3}}{2}$ ix + (3- $\frac{\sqrt{3}}{2}$ i)(3+ $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{\sqrt{3}}{2}$ i)( $\frac{\sqrt{3}}{2}$ i) ] =0