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Sagot :
GIVEN:
We are given two equations as shown below;
[tex]\begin{gathered} y=\frac{3}{4}x-5----(1) \\ \\ y=\frac{4}{3}x+2----(2) \end{gathered}[/tex]Required;
To determine if the equations are parallel lines, perpendicular lines, or neither of the two.
Explanation:
For any given line in the slope-intercept form,
[tex]y=mx+b[/tex]we can determine if they are parallel or perpendicular by examining the slope of the line.
The slope is given as the coefficient of x. Take note also, that the slopes of two parallel lines must always be EQUAL to each other. And for perpendicular lines, the slopes must be NEGATIVE INVERSE of each other.
The slopes of the lines given are;
[tex]\begin{gathered} m_1=\frac{3}{4} \\ \\ m_2=\frac{4}{3} \end{gathered}[/tex]Notice carefully that slope 2 is NOT EQUAL to slope 1, and neither is it a negative inverse of the other
Therefore,
ANSWER:
NEITHER
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