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Which linear inequality is represented by the graph?


y ≤ x – 1.3

y ≤ x – 4/3

y ≥ x – 4/3

y ≥ x – 1.3

Which linear inequality is represented by the graph? y x 1.3 y x 4/3 y x 4/3 y x 1.3 class=

Verified Answer :

calculista

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

View image calculista
View image calculista
View image calculista
View image calculista

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.

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