Question

2. Given a point (−3,6) and a line y = 2x − 8:

a. What is the slope of the line?
b. What is the slope of any line parallel to the given line?
c. Write an equation of a line through the point and parallel to the line.
d. What is the slope of any line perpendicular to the given line? Explain.

Answer 1

a. 2

b. 2

c. y = 2x +12

d. -1/2

Explanation:

a. The equation of the given line matches the form ...

y = mx + b

with m=2 and b=-8. "m" is the slope of the line, so the slope is 2.

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b. Any parallel line will have the same slope, 2.

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c. The desired equation can be written several ways. One of the ways you can approach this is to use the slope-intercept form above and fill in the given values. Then solve for the unknown b.

6 = 2(-3) +b

12 = b . . . . . . . . . . add 6 to both sides

Then the equation of the line with slope 2 through point (-3, 6) is ...

y = 2x +12

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d. The slope of a perpendicular line is the negative reciprocal of the slope of the line to which it is perpendicular. The negative reciprocal of 2 is -1/2.

The slope of any perpendicular is -1/2.