Find the equation of the line which passes through the point (4,-2)
and which is perpendicular to the line 3y -2x = -6.

Visualize the problem:

Find two points on the line 3y -2x = -6 and sketch the line.
Also, plot the point (4,-2).
Sketch the line through (4,-2) and perpendicular to 3y -2x = -6.

Find two points on the line 3y -2x = -6. Suggestion:
Find the y coordinates corresonding to x = 0 and x = 3.

Plot these two points and sketch the line passing through them.
Also plot the point (4,-2) and sketch the line through (4,-2) and
perpendicular to 3y -2x = -6.

Continuing Strategy: 1.Find the slope of the 3y -2x = - 6 (i.e. the solid line)
2.Deduce the slope of the perpendicular line (i.e. the dotted line).
3. Use the point slope formula to find the equation of the perpendicular line.

Find the slope of the line 3y -2x = - 6 (i.e. the solid line in the figure.) by solving this equation for y.

The slope of the perpendicular
line is the negative reciprocal of the above slope. - i.e.

Deduce the slope of perpendicular line(i.e. the dotted line).

Show work.

Find the equation of the perpendicular line by using the
point-slope equation for a line.

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