Question

Which linear inequality is represented by the graph?

y ≤ x – 1.3
y ≤ x – 4/3
y ≥ x – 4/3
y ≥ x – 1.3

Answer 1

We will proceed to graph each case to determine the solution of the problem.

case a) $y\leq x - 1.3$

Using a graph tool

see the attached figure N $1$

The solution is the shaded area

The inequality of the case a) is not  represented by the graph

case b) $y\leq(x - 4)/3$

Using a graph tool

see the attached figure N $2$

The solution is the shaded area

The inequality of the case b) is represented by the graph

case c) $y \geq(x -4)/3$

Using a graph tool

see the attached figure N $3$

The solution is the shaded area

The inequality of the case c) is not  represented by the graph

case d) $y \geq x -1.3$

Using a graph tool

see the attached figure N $4$

The solution is the shaded area

The inequality of the case d) is not  represented by the graph

therefore

the answer is

The inequality $y \leq (x - 4)/3$ is represented by the graph

Answer 2

The line represents the inequality y $\leqslant$ $\frac{1}{3}x-1.3$. Hence, $\boxed{{\text{Option A}}}$ 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 inequalities are as follows.

A. y $\leqslant$ $\frac{1}{3}x-1.3$.

B. y $\leqslant$ $\frac{1}{3}x-\frac{4}{3}$.

C. y $\geqslant$ $\frac{1}{3}x-\frac{4}{3}$.

D. y $\geqslant$ $\frac{1}{3}x-1.3$.

Explanation:

The line intersects y-axis at $\left({0,-1.3}\right)$, therefore the y-intercept is -1.3.

The points are $\left({0,-1.3}\right)$ and $\left({3,-0.3}\right)$.

The slope of the line can be obtained as follows.

$\begin{aligned} m&=\frac{{-0.3-\left({-1.3}\right)}}{{3-0}}\\&=\frac{{-0.3+1.3}}{3}\\&=\frac{1}{3}\\\end{aligned}$

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

Now check whether the inequality included origin or not.

Substitute $\left({0,0}\right$) in the option A.

$\begin{aligned} 0\leqslant\frac{1}{3}\left(0\right)-1.3\hfill\\0\leqslant-1.3\hfill\\\end{aligned}$

0 is not less than -1.3 which means that the inequality doesn’t includes origin.

The line represents the inequality y $\leqslant$ $\frac{1}{3}x-1.3$. $\boxed{{\text{Option A}}}$ is correct.

Option B is not correct as the y-intercept is not -1.3.

Option C is not correct as the y-intercept is not -1.3.

Option D is not correct as the inequality doesn’t include the origin.

Hence, $\boxed{{\text{Option A}}}$ is correct.

Learn more:

1. Learn more about inverse of the function https://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 https://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.