Answer :
Using linear function concepts, it is found that the two lines can be classified as:
(4) intersecting, but not perpendicular.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope defines if the lines are parallel or perpendicular, as follows:
- If they are parallel, they have the same slope.
- If they are perpendicular, the multiplication of the slopes is of -1.
- If the multiplication of -1, and the slopes are different, they are intersecting.
In this problem, the lines in slope-intercept formula are:
[tex]y = \frac{2}{3}x - 2 \rightarrow = m = \frac{2}{3}[/tex]
[tex]y = \frac{3}{2}x + 3 \rightarrow m = \frac{3}{2}[/tex]
Then:
[tex]\frac{2}{3} \times \frac{3}{2} = 1[/tex]
So they are intersecting and not perpendicular, which means that option 4 is correct.
More can be learned about linear function concepts at https://brainly.com/question/24808124
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