Answer:
(a) The parallel line is y = -4x + 19
(b) The perpendicular line is y = (1/4)x + 1.5
Explanation:
The question is slightly unclear. Lets assume that a reference line is given that intersects points (1,6) and (2,2). Lets start with this find an equation of this reference line.
We'll look for a line in slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
Slope, m, is the "Rise/Run) between two points. Take the two given points and calculate the slope as one moves from lower to higher values of x:
Reference Line: (1,6) to (2,2)
Rise = (2 - 6) = -4
Run = (2 - 1) = 1
Slope is Rise/Run = (-4/1) or -4
The line takes the form y = -4x + b.
To find b, enter one of the points in the equation and solve for b:
y = -4x + b
2 = -4*2 + b for (2,2)
b = 10
The reference line is y = -4x + 10.
See the attached graph for this line.
The question appears to be asking for the equations of two lines:
a) One that is parallel to the reference line, and
b) one that is perpendicular to the reference line.
Two key factors in making this work:
1) Parallel lines have the same slope
2) Perpendicular lines have slopes that are the negative inverse of each other (e.g., a slope of 2 becomes a slope of -(1/2))
For each question:
a) A parallel line will have the same slope, and will therefore take the form of y = -4x + b
b) A perpendicular line with have the negative inverse of the reference line slope, and will therefore take the form of y = (1/4)x + b
To find the values of b for each line, do as before. Use one of the two given points and solve for b for each line.
a) y = -4x + b
3 = -4*4 + b for (4,3)
b = 19
The parallel line is y = -4x + 19
b) y = (1/4)x + b
We will assume the question wants this line to also pass through point (2,2)
2 = (1/4)*2 + b for (2,2)
b = 1.5
The perpendicular line is y = (1/4)x + 1.5
See the attached graph.