Question

Which linear inequality is represented by the graph?

A. y ≤ 1/3 x – 1.3
B. y ≤ 1/3 x –4/3
C. y ≥ 1/3 x –4/3
D. y ≥ 1/3 x – 1.3

Answer 1

The correct answer is A. y ≤ 1/3x - 1.3.

Firstly, we see that the shaded region is *below* the line. This means that the equation is going to be ≤, not ≥. If it was ≥, then the shaded region would be above the line. Therefore, this eliminates C & D.

Next, the inequality is in slope-intercept form, which is y = mx+b, with m = slope and b = y-intercept. With this line, you see that the y-intercept is (0, -1.3). Therefore, this eliminates B & C.

And by process of elimination, the correct answer is A.

Answer 2

The line represents the inequality y$\leqslant \dfrac{1}{3}x - 1.3$. 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 $\leqslant \dfrac{1}{3}$x - 1.3.

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

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

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

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 $m = \dfrac{1}{3}$.

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 $\leqslant \dfrac{1}{3}x - 1.3. \boxed{{\text{Option A}}}$ 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 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 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.