Mathematics, 26.07.2019 23:30 carlo123

Which system of linear inequalities is represented by the graph? y > x + 3 and 3x – y > 2 y > x + 3 and 3x – y > 2 y > x + 3 and 3x + y > 2 y > x + 3 and 2x – y > 2

Which system of linear inequalities is represented by the graph? y > x + 3 and 3x – y > 2 y

Answers: 2

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Answer from: hhgjhbmbhg266

Step 1: Find equations of the lines
Red, solid line:
Find slope: 1square in y / 3 squares in x => slope = 1/3
y-intercept : (0,3)
Equation of the line: one of the following:
y=x/3+3 (1a)
3y=x+9 (1b)
x-3y+9=0 (1c)
Black, dotted line:
Slope = 3 squares in y / 1 square in x => slope = 3
y-intercept (0,-2)
Equation of the line: one of the following:
y=3x-2(2a)
3x-y=2(2b)

2. Find location of region, i.e. greater or less than
Red region:
The region is above the solid line, i.e. we look for y>=
From equation (1a), we change the equality to >=, or
y >= x/3+3 [>= because line is solid]
Black region:
The region is to the right of the dotted line, we look for x > ...
From equation (2b),, we change equality to >, or
3x-y > 2 [ > because line is dotted ]

Note: All the given answers have common typos, namely
the first inequality should read y > x/3+3 or y>=x/3+3
the second inequality should read 3x-y > 2 or 3x-y >=2
The way question is presented, all the answer choices are the same (and incorrect).

@lazalewagoner you still have time to correct the answer choices.

Answer from: izzzzz49

The lines represent the inequalities $\boxed{y\frac{1}{3}x + 3{\text{ and }}3x - y 2.}$ .

Further explanation:

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}}\right)$ and $\left( {{x_2},{y_2}}\right)$ can be expressed as,

$\boxed{m=\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Given:

The inequalities are as follows.

a. $y x + 3{\text{ and }}3x - y 2$

b. $y x + 3{\text{ and }}3x - y 2$

c. $y x + 3{\text{ and }}3x + y 2$

d. $y x + 3{\text{ and 2}}x - y 2$

Explanation:

The blue line intersects y-axis at (0, - 2) , therefore the y-intercept is .

The blue line intersect the points that are $\left( {1,1} \right)$ and $\left( {0, - 2}\right)$ .

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{1 -\left({- 2} \right)}}{{1 - 0}}\\&=\frac{{1 + 2}}{1}\\&=3\\\end{aligned}$

The slope of the line is m = 3 .

Now check whether the inequality included origin or not.

Substitute $\left( {0,0}\right)$ in equation y < 3x - 2 .

$\begin{aligned}\left( 0 \right) &< 3\left( 0 \right)- 2\\0 &< - 2\\\end{aligned}$

0 is not less than which mean that the inequality doesn’t include origin.

Therefore, the blue line is $y < 3x--2{\text{ or }}3x - y 2$ .

The orange line intersects y-axis at $\left( {0,3}\right)$ , therefore the y-intercept is 3.

The orange line intersect the points that are $\left( { - 3,2}\right)$ and $\left( {0,3}\right)$ .

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{3 - 2}}{{0 - \left( { - 3}\right)}}\\&=\frac{1}{3}\\\end{aligned}$

The slope of the line is $m = \dfrac{1}{3}$ .

Now check whether the inequality included origin or not.

Substitute $\left( {0,0}\right)$ in equation $y \dfrac{1}{3}\left( x \right) + 3$ .

$\begin{aligned}\left(0 \right)&\frac{1}{3}\left(0\right) + 3\\0&3\\\end{aligned}$

0 is not greater than 3 which mean that the inequality doesn’t include origin.

Therefore, the orange line is $y \dfrac{1}{3}x + 3$ .

The lines represent the inequalities $\boxed{y \frac{1}{3}x + 3{\text{ and }}3x - y 2.}$ .

Learn more:

1. Learn more about inverse of the functionhttps://link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

Answer from: Quest

Ithink the answer is a

Answer from: Quest

answer: at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

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Which system of linear inequalities is represented by the graph? y > x + 3 and 3x – y > 2 y...