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.