Graph A is correct.
We have an inequality -
[tex]y < \frac{3x}{4}+2[/tex]
We have to graph this inequality and select the correct option.
What is inequality?
Inequality in mathematics is a relation that is used to compare two or more algebraic expressions.
We have in our question an inequality as -
[tex]y < \frac{3x}{4}+2[/tex]
Follow the following steps to reach the graph -
STEP 1 ->
Replace the ' < ' sign with ' = ' sign and plot the graph of the equation formed - [tex]y = \frac{3x}{4}+2[/tex]
which is same as y = mx + c.
On comparing : m = [tex]\frac{3}{4}[/tex] and c =2.
Therefore, this line intersects the y - axis at the point (0, 2).
STEP 2 ->
Since the line does not pass through (0,0) we can consider it as our test point. Substituting x = y = 0 in the inequality, we get -
0 < 0 + 2
0 < 2, which is true.
We will shade the area in which (0,0) lies.
STEP 3 ->
Since the inequality is a strict inequality, the line will be a dotted line.
Hence, Graph A is correct.
To solve more questions on plotting the graphs of inequality, visit the link below -
https://brainly.com/question/25851784
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