Question

.
In which quadrants do solutions for the inequal
the inequality
$y \leqslant \frac{2}{3}x - 4$
exist.


A.I, III, and IV
B.I, II, and III
C.I and IV
D.All four quadrants​

Answer 1

Answer:

A.I, III, and IV

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

If m > 0, then the function is increased

If m < 0, then the function is decreased

We have

$m=\dfrac{2}{3}>0$ - the function is increased

$b=-4$ - the y-intercept is -4 → (0, -4)

Therefore the line passes through III, IV and I quadrant.

========================================

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

========================================

We have $y\leq\dfrac{2}{3}x-4$ → ≤ - shaded region below the line.

Therefore the inequal the inequality exist in I, III and IV quadrant.

Look at the picture.

Answer 2

The inequality exists in quadrants A.I, III, and IV.

The answer is option A

What is a straight line graph?

• The graph follows a straight line equation shows a straight line graph.

• equation of a straight line is   y=mx+cy represents vertical line y-axis.

• x represents the horizontal line x-axis.    

• m is the slope of the line

            slope(m)=tan∅=y axis/x axis.

If m > 0, then the function is increased

If m < 0, then the function is decreased

=function is increased

=y-intercept is -4 = (0, -4)

    Therefor the line passes through III, IV and I quadrant.

• c represents y-intercepts (it is the point at which the line cuts on the y-axis)

• Straight line graphs show a linear relationship between the x and y values.

     

Learn more about quardinate geomtry here:-https://brainly.com/question/18269861

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