Two lines are perpendicular when the product between the slopes of the lines is equal to -1, then, if we have the following lines:
[tex]\begin{gathered} y_1=m_1x+b_1 \\ y_2=m_2x+b_2 \end{gathered}[/tex]they will be perpendicular if,
[tex]m_1\cdot m_2=-1[/tex]According to the exercise, the first line is:
[tex]y=-4x+7[/tex]the slope for this line is -4.
Write the equation that makes two lines perpendicular,
[tex]-4\cdot m_2=-1[/tex]solve for m2,
[tex]\begin{gathered} m_2=\frac{-1}{-4} \\ m_2=\frac{1}{4} \end{gathered}[/tex]Answer:
The slope of the line perpendicular to y=-4x+7 is 1/4.
