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Line m passes through point (–2, –1) and is perpendicular to the graph of y = –23x + 6. Line n is parallel to line m and passes through point (4, –3). Which is the equation of line n in slope-intercept form?

1 Answer

1 vote


\huge\boxed{y=(1)/(23)x-(73)/(23)}

First, find the slope perpendicular to
-23. We can do this by finding the opposite reciprocal.

Multiply the slope by
-1 and write the result as a fraction.


-23*-1=23=(23)/(1)

Flip the numerator and the denominator.


(23)/(1)\longrightarrow(1)/(23)

This is the slope of line
m. Since lines
m and
n are perpendicular, this is also the slope of line
n.

Write the formula for point-slope form.


y-y_1=m(x-x_1)

Substitute in the values for line
n.


y-(-3)=(1)/(23)(x-4)

Simplify the negative subtraction.


y+3=(1)/(23)(x-4)

Distribute the
(1)/(23) to the
(x-4).


y+3=(1)/(23)x-(4)/(23)

Subtract
3 — which is equivalent to
(69)/(23) — from both sides.


\boxed{y=(1)/(23)x-(73)/(23)}

User Rogach
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