Question

Which linear inequality is represented by the graph?

Answer 1

Answer:

$y\leq \frac{1}{3}x-1.3$

Explanation:

First we find the slope of the line that passes through the two given points.  The formula for slope is

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

Using our two points, we have

$m=\frac{-0.3--1.3}{3-0}=\frac{-0.3+1.3}{3-0}=\frac{1}{3}$

The y-intercept of a line is the point where it crosses the y-axis.  The graph gives us this; it is -1.3.

In slope-intercept form, this gives us the equation $y=\frac{1}{3}x-1.3$.

The graph is shaded below this line and the line is solid.  This means the inequality is less than or equal to, giving us

$y\leq \frac{1}{3}x-1.3$

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.

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.