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Tasya [4]
3 years ago
10

Which linear inequality is represented by the graph? (A)y ≤1/3 x − 1 (B)y ≥ x − 1 (C)y < 3x − 1 (D)y > 3x − 1

Mathematics
2 answers:
lubasha [3.4K]3 years ago
7 0

The equation of the line is \boxed{y \geqslant \frac{1}{3}x - 1}.

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:

Explanation:

The line intersects y-axis at \left( {0, - 1} \right). Therefore, the y-intercept is -1.

The line passes through the points \left( {0, - 1} \right) and \left( {3,0} \right).

The slope can be obtained as follows,

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

Substitute \dfrac{1}{3} for m, 3 for x and 0 for y in equation y = mx + c to obtain the value of c.

\begin{aligned}0& \frac{1}{3} \cdot 3 + c\\- 1&=c\\\end{aligned}

To check whether the equation includes origin substitute 0 for x and 0 for y in equation y \geqslant \dfrac{1}{3}x - 1.

\begin{aligned}0&\geqslant \frac{1}{3} \times 0 - 1 \\0&\geqslant - 1\\\end{gathered}

The statement is true. The equation contains origin.

The equation of the line is \boxed{y \geqslant \frac{1}{3}x - 1}.

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 equation

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

makvit [3.9K]3 years ago
6 0

Linear inequality represented by the graph is

\displaystyle (A)y\geq \dfrac{1}{3}x-1

<h3>Further explanation </h3>

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

 \large{\boxed{\bold{y-y_1=m(x-x_1)}}

or

<h3> y = mx + c </h3>

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points  

\large{\boxed{\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}}

If the intersection of the x-axis (b, 0) and the y-axis (0, a) then the equation of the line:

<h3> ax + by = ab </h3>

It says inequality if there are symbol forms like <, >, ≤ or ≥

Whereas linear inequality can have forms:  

<h3>ax + by> c, ax + by ≥ c , ax + by <c , ax + by ≤ c </h3>

In graphical form, line inequality can be

  • dashed line because y does not include equals to
  • a solid line because y includes equal to

For line inequality (positive coefficient y)

ax + by ≥ c then the solution is shaded upwards

ax + by ≤ c then the solution is shaded down

Or we input the values ​​x, y from the point in the shaded area and put in the inequality line

From the picture we can determine the equation of the line

Line through 2 points (3,0) and (0,-1)

the gradient:

\displaystyle m=\frac{-1-0}{0-3}\\\\\displaystyle m=\frac{1}{3}

the equation of the line:  point (3,0)

\displaystyle y-0=\frac{1}{3}(x-3)\\\\\displaystyle y=\frac{1}{3}x-1

We check the point in the area of ​​shading, for example (0, 0)

we input in the equation :

\displaystyle 0=\frac{1}{3}.0-1\\\\0=-1

Because 0 > -1 and the graph is solid line so the inequality line will be

\displaystyle (A)y\geq \dfrac{1}{3}x-1

 

<h3>Learn more </h3>

F (x) = x2 + 1 g (x) = 5 - x

htps: //brainly.com/question/2723982

the inverse of the function f (x) = 2x-10

brainly.com/question/628130

domain of the function

brainly.com/question/4135536

Keywords: linear inequality,graph

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