Find the slope of the perpendicular line:
[tex]y = \dfrac{1}{2} x + b[/tex]
[tex]\text {Slope = } \dfrac{1}{2} [/tex]
[tex]\text {Slope =} \boxed {\text{negative reciprocal}} \text { of the slope of the original line}[/tex]
[tex]\text {Perpendicular Slope = -2}[/tex]
Form the equation:
[tex]y = mx + b[/tex]
[tex]y = -2x + b[/tex]
Find y-intercept given that the line passed through (-4, 7):
[tex]y = -2x + b[/tex]
[tex]7 = -2(-4) + b[/tex]
[tex]7 = 8 + b[/tex]
[tex]b = 7 - 8[/tex]
[tex]b = -1[/tex]
Form the equation:
[tex]y = -2x - 1[/tex]
[tex]\boxed {\boxed {Answer: y = -2x - 1}}[/tex]
