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Given: line 1 passes through (-3, -7) and (5,3)

Line 2 passes through (-4, -2) and is perpendicular to line 1

User Carlyne
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Answer:

Explanation:

We start by developing an equation for Line 1, and then use that to find the equation for Line 2. We'll use the form of an equation for a straight line:

y = mx + b,

where m is the slope and b the y-intercept (the value of y when x=0).

Line 1

Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).

Line up the two points from left to right (based on x) and then calculate:

Rise: (3 - (-7)) = 10

Run: (5 -(-3) = 8

The slope, m, is Rise/Run or (10/8)

The equation becomes y = (5/4)x + b

We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m. Slope is (5/4), which we'll use in the next step: Line 2.

[Note: Out of curiosity, here is the calculation for b: Use point (5,3) in y = (5/4)x + b and solve for b. 3 = (5/4)*5 + b. 3 = (25/4) + b b = -13/4. This means that Line 1 is y = (5/4)x -(13/4)]

Line 2

The slope of a line perpendicular to the first is the "negative inverse" of the first line. In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.

Line 2: y = -(8/13)x + b

We'll calculate b for this line by enetering the single point provided, (-4,-2), and solving for b:

y = -(8/13)x + b

-2 = -(8/13)*(-4) + b

-2 = (32/13) + b

-2 - (32/13) = b

b = -(26/13) - (32/13)

b = -(58/13)

The new line perpendicular to Line 1 and passing through (-4,-2) is:

y = -(8/13)x -(58/13)

See attached graph.

Given: line 1 passes through (-3, -7) and (5,3) Line 2 passes through (-4, -2) and-example-1
User Alexpopescu
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