To find angle between two lines, we use the formula,
[tex]\tan \theta=\frac{m_1-m_2}{1+m_1m_2}[/tex]Where
θ is the angle between two lines
m1 is the slope of the first line
m2 is the slope of the second line
First Line Equation:
[tex]\begin{gathered} 3x-my=15 \\ my=3x-15 \\ y=\frac{3}{m}x-\frac{15}{m} \end{gathered}[/tex]The slope is 3/m
Second Line Equation:
[tex]\begin{gathered} 3x+5y=7 \\ 5y=-3x+7 \\ y=-\frac{3}{5}x+\frac{7}{5} \end{gathered}[/tex]The slope is -3/5
The angle between the two lines is 45°.
Let's substitute the known information into the formula and figure out the value of 'm':
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