If two lines of slopes m1 and m2 are perpendicular, then:
[tex]m_1\cdot m_2=-1[/tex]The slope of a line passing through points (x1, y1) and (x2, y2) is:
[tex]\begin{equation*} m=\frac{y_2-y_1}{x_2-x_1} \end{equation*}[/tex]We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope
[tex]m_1=\frac{3-7}{1+4}=-\frac{4}{5}[/tex]The slope of the perpendicular line is:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{4}{5}}=\frac{5}{4}[/tex]The equation of the perpendicular line has the form:
[tex]y=\frac{5}{4}x+b[/tex]None of the options has the correct answer.
