The linear equality represented by the graphis
and it matches with
.
Further explanation:
It is given that a line passes through points
and
as shown below in Figure 1
The slope of a line passes through points
and
is calculated as follows:
......(1)
Here, the slope of a line is denoted as
and points are
and
.
Substitute
for
,
for
,
for
and
for
in equation (1) to obtain the slope of a line that passes through points
and
.
![\begin{aligned}m&=\frac{{ - 7 - 2}}{{ - 3 - 0}}\\&=\frac{{ - 9}}{{ - 3}}\\&=3\\\end{aligned}](/tpl/images/0389/8546/2127a.png)
Therefore, the slope is
.
The point-slope form of the equation of a line with slope
passes through point
is represented as follows:
......(2)
Substitute
for
,
for
and
for
in equation (2) to obtain the equation of line.
![\begin{aligned}y - 2&=3\left({x - 0}\right)\\y - 2&=3x\\y&=3x + 2\\\end{aligned}](/tpl/images/0389/8546/12ad4.png)
Therefore, the value of
is
.
Since the shaded part in Figure 1 is above the equation of line
, therefore, greater than sign is used instead of is equal to.
Thus, the linear inequality is
as shown below in Figure 2.
Now, the four options are given below.
![\begin{aligned}{\text{OPTION A}} \to y < 3x + 2 \hfill\\{\text{OPTION B}} \to y 3x + 2 \hfill\\{\text{OPTION C}} \to y < x + 2 \hfill\\{\text{OPTION D}} \to y x + 2 \hfill\\\end{aligned}](/tpl/images/0389/8546/fbb37.png)
Since OPTION B matches the obtained equation that is
.
Thus, the linear equality represented by the graph is
and it matches with
.
Learn more:
1. Which classification best describes the following system of equations?
2. What is the value of in the equation when ?
3. What are the values of x?
Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords:Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point, inequality
![Which linear inequality is represented by the graph? y < 3x + 2 y > 3x + 2 y < x + 2 y](/tpl/images/0389/8546/875ae.jpg)
![Which linear inequality is represented by the graph? y < 3x + 2 y > 3x + 2 y < x + 2 y](/tpl/images/0389/8546/022d0.jpg)