Answer:
1. Find the equation, in slope intercept form, of the straight line joining the point (-5,7)and(1/2,29)
b. find the equation in slope intercept form, of the perpendicular bisector of the straight line segment joining the point (-5,7)and (1/2,29)
2. solve the linear inequality and leave the answer in interval notation.9x/5+32 greater then equal 5/9 (x-32)
Step-by-step explanation:
st find the slope f the line that connects the two points (-5, 7) and (1/2, 29) using the following slope formula:
I) Slope(m) = y2 - y1 / x2 - x1 = 29 - 7 / 1/2 - (-5) = 22 / 5.5 =4
II) Second step is to plug one of the points (your choice) and the slope into the point slope formula:
y - y1 = m ( X - x1) Use the point (-5 , 7) since it has no fractions and will be easier to plug in. Plug 7 in for y1 and -5 for X1.
y - 7 = 4(x - -5)
y - 7 = 4(x + 5) Now distribute on right side and isolate "y" to get eq. in slope intercept form.
y - 7 = 4x + 20 Add 7 to both sides to isolate "y"
+7 + 7
y = 4x + 27 This is the slope intercept form of the equation.
1b) To find the equation of the line of the perpendicular bisector, you will need to bisect the original line which means to intersect the original line at it's midpoint. The midpoint can
be found using the following formula: Midpoint (Mx , My) Mx = x1 + x2 / 2 and My = y1 + Y2 / 2
Mx = -5 + 1/2 / 2 = -4.5 / 2 = -2.25 = -2 1/4 = -9/4
My = 7 + 29 / 2 = 36 / 2 = 18
Midpoint is (-9/4 , 18) You will use this point when you write your EQ. for the perpendicular bisector.
Next to bring perpendicularity into the plan, we must remember that when lines are perpendicular to each other, their slopes are opposite signed reciprocals. So if your original slope is 4, then your perpendicular slope is -1/4. Now we have a point and a slope for our perpendicular bisector EQ.
Finally, use the Point slope eq. given in step II of problem 1a
y - y1 = m(x - x1) Use the midpoint coordinates for x1 and y1
y - 18 = -1/4( x - -9/4)
y - 18 = -1/4(x + 9/4) Now distribute the -1/4 and isolate y.
y - 18 = -1x/4 - 9/16 Now add 18 to both sides to isolate y
+18 +18
y = -1x/4 + 279/16
2) To solve the inequality 9x/5 + 32 > 5/9(x - 32) First multiply entire inequality by LCD 45, which is smallest number that both denominators 5 and 9, divide into.
45[ 9x/5 + 32 > 5/9(x - 32) ]
45(9x/5) + 45(32) > 45(5/9)(x-32)
81x + 1440 > 25(x - 32) Now distribute 25
81x + 1440 > 25x - 800 Move 25x to the left by subtracting 25x from both sides
-25x -25x
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56x + 1440 > -800 Now subtract 1440 from both sides
-1440 -1440
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56x/56 > -2240/56 Now divide both sides by 56
x > -40
