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Write an equation of the line in slope-intercept form that passes through $\left(4,\ 3\right)$ and is (a) parallel and (b) perpendicular to the line shown. Graph of a line on a coordinate plane. The line passes through the points, ordered pair 1 comma 6 and ordered pair 2 comma 2.

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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.

Write an equation of the line in slope-intercept form that passes through $\left(4,\ 3\right-example-1
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