An equation that represents a line that is perpendicular to the given line is [tex]2y=3x+1[/tex].
Given the following data:
[tex]y=\frac{2}{3} x+1[/tex]
To determine an equation that represents a line that is perpendicular to the given line:
In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).
Mathematically, this is given by the formula:
[tex]m_1 \times m_2 = -1[/tex]
Note: Slope, [tex]m_1[/tex] = [tex]\frac{2}{3}[/tex]
Substituting the given parameters into the formula, we have;
[tex]\frac{2}{3} \times m_2=-1\\\\2m_2=-3\\\\m_2=\frac{3}{2}[/tex]
For the perpendicular line:
[tex]y=mx+b\\\\y=\frac{3}{2}x +1\\\\2y=3x+1[/tex]
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