Question

Line k is graphed at right.

Write an equation of a line parallel to K
Write an equation of a line perpendicular to K

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Answer 1

See below ↓↓

Explanation:

Equation of line k

• y = mx + b
• m = Δy/Δx (ratio of change in y to change in x) = 2/3
• b = 3 (as y-intercept is [0,3])
• ⇒ y = 2/3x + 3

a. parallel line

• For parallel lines, slope (m) remains the same, but the y-intercept (b) changes
• ⇒ y = 2/3x + 1

b. perpendicular line

• For perpendicular lines, the slope (m) is the negative reciprocal of the original line and the value of b stays the same [it can be any point as long as it intersects the line]
• ⇒ y = -3/2x + 1