To write the equation of the line in , we need its slope and its
y-intercept. To ensure the lines are perpendicular, their slopes,
m1 and
m2, must multiply to equal
-1. m1⋅m2=-1
The given line has the slope
m1=32. Thus, we can use the product to determine
m2.
m1⋅m2=-1 32⋅m2=-1 2⋅m2=-3 m2=-23
The slope of the other line is
m=-23, so we can write the incomplete equation of this line as
y=-23x+b.
Recall that the line must pass through the point
(0,-1). To find the
y-intercept, we can substitute the point
(0,-1) for
x and
y in the incomplete equation above.
y=-23x+b -1=-23⋅0+b
The
y-intercept of the line is
b=-1. This gives the equation
y=-23x−1.