Question

Which system of linear inequalities is represented by the graph?

Answer 1

The system of linear inequalities is represented by the graph are $\boxed{y > x - 2}$ and $\boxed{y < x + 1}.$ Option (a) is correct.

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,

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

Given:

The given options are as follows,

(a). $y > x - 2{\text{ and }}y < x + 1$

(b). $y < x - 2{\text{ and }}y > x + 1$

(c).$y < x - 2{\text{ and }}y > x + 1$

(d). $y > x - 2{\text{ and }}y < x + 1$

Explanation:

The first line passes the points $\left( {0, 1}\right)$ and $\left( {-1,0}\right).$

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{0 - 1}}{{0 - 1}}\\&=\frac{{ - 1}}{{ - 1}}\\ &= 1\\\end{gathered}$

The slope of the line is $m = 1.$

The line intersect y-axis at $\left( {1,1}\right)$. Therefore, y-intercept is 1.

Substitute $\left( {0,0}\right)$ in equation $y< x+1$ to check whether the equation includes origin.

$\begin{aligned}0&$

The equation of first line is $y < x + 1.$

The second line passes the points $\left( {0, -2}\right)$ and $\left({2,0}\right).$

The slope of the line can be obtained as follows.

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

The slope of the line is $m = 1.$

The line intersect y-axis at $\left( {-2,0} \right).$ Therefore, y-intercept is -2.

Substitute $\left( {0,0}\right)$ in equation $y > x - 2$ to check whether the equation includes origin.

$\begin{aligned}0&> 0- 2\\0&> - 2\\\end{aligned}$

The equation of second line is $y > x -2.$

The system of linear inequalities is represented by the graph are $\boxed{y > x - 2}$ and $\boxed{y < x + 1}.$

Option (a) is correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

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

Answer 2

Hmm, find the lines

they both seem to have a slope of 1
the top one has a y intecept at 1 and the bottom one at -2

y=x+1 and y=x-2
ok, so they both have (0,0) in them

so if ? represents an inequality sign
y ? x+1
0 ? 0+1
0 ? 1
0<1
so y<x+1 is one of the equations

y ? x-2
0 ? 0-2
0 ? -2
0>-2
so y>x-2

y>x-2 and y<x+1

first one