Question

Which linear inequality is represented by the graph? y > 2x + 3 y < 2x + 3 y > −2x + 3 y < −2x + 3

Answer 1

The line represents the inequality $\boxed{y < - 2x + 3}.$ Option (d) 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 inequalities are as follows.

(a). $y > 2x + 3$

(b). $y < 2x + 3$

(c). $y > - 2x + 3$

(d). $y < - 2x + 3$

Explanation:

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

The points are $\left( {0,3} \right)$ and $\left( {1,1} \right).$

The slope of the line can be obtained as follows.

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

The slope of the line is $m = 2.$

Now check whether the inequality included origin or not.

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

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

0 is less than 3 which means that the inequality does include origin.

Kindly refer to the image attached.

The line represents the inequality $\boxed{y < - 2x + 3}.$ Option (d) is 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 inequalities

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

Answer 2

You haven't provided the graph, therefore, I can only help with the concept.

First, you need to define the line drawn:

Equation of line is: y=mx + c

where:

m is the slope = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

c is the y-intercept which is the value of the y at x = 0

The, you need define the shaded region:

To do so, take any point from the graph and substitute in the inequality, if it satisfies the inequality, then, it is within the shaded region, otherwise, it is not.

Hope this helps :)