Question

Which linear inequality is represented by the graph?

Answer 1

In the given graph the line is having the y intercept as -4.

The slope of line = $\frac{Rise}{Run} =\frac{1}{3}$

The equation of the line is $y=\frac{1}{3}x-4$

The line is a dark line so inequality will be either ≤ or ≥.

Consider point (0,-5)which lie in the shaded region.

Plug x=0 and y=0 in the equation of line,

-5=$\frac{1}{3}(0)-4=-4$

-5≤ -4 .

The inequality equation for the given graph is

y≤$\frac{1}{3}x-4$

Answer 2

Linear inequality represented by the graph is

$\displaystyle y\leq \frac{1}{3}x-4$

Further explanation

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

General formula

$\large{\boxed{\bold{y-y1=m(x-x1)}}$

or

y = mx + c

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  

$\large{\boxed{\bold{m= \frac{y2-y1}{x2-x1}}}$

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

ax + by = ab

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

• Whereas linear inequality can have forms:  ax + by> c ax + by ≥ c ax + by <c ax + by ≤ c

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 (0, -4) and (-3, -5)

the gradient: $\displaystyle =\frac{-5+4}{-3-0}\\\\=\frac{1}{3}$

the equation of the line:

$\displaystyle y-y1=m(x-x1)\\\\y+4=\frac{1}{3}(x-0)\\\\=\frac{1}{3}x-4$

We check the point in the area of ​​shading, for example (0, -6)

we input in the equation :

$\displaystyle -6=\frac{1}{3}.0-4\\\\-6=-4$

Because -6 < -4 and the graph is solid line so the inequality line will be

$\displaystyle y\leq \frac{1}{3}x-4$

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Keywords: linear inequality,graph