Write the point-slope equation of the line that passes through(3,5) and (7,1)
1 answer:
Answer: y - 1 = –(x –7)
or y –5 = –1(x –3)
The attachment shows the graph of these equations (identical)
Step-by-step explanation:
The basic form for a point-slope equation is
y - b = m(x - a)
a is the x-value from the given coordinate, b is the y-value form the given coordinate, m is the slope. x and y are the variables in the function.
To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."
Subtract the first coordinate from the second coordinate.
Given coordinate points: (3,5) and (7,1) substitute values:
m= 1 –5 / 7 –3 becomes m= –4/4 so the slope, m = –4/4
That is –1 The "1" is "understood," so only the negative sign represents the slope in the equation
To write the equation: Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.
y - b = m(x - a) Using the second coordinate: (7,1)
y - 1 = –(x –7)
or using the first coordinate:
y –5 = –(x –3)
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Answer:
The solution to the box is
a = 2.1
b = 5.9
c = 0.9
d = 10
Step-by-step explanation:
To answer the equation, we simply name the boxes a,b,c and d.
Such that
a + b = 8 ---- (1)
b - c = 5 ------ (2)
d * c = 9 ------ (3)
a * d = 21 ------- (4)
Make d the subject of formula in (3)
d * c = 9 ---- Divide both sides by c
d * c/c = 9/c
d = 9/c
Substitute 9/c for d in (4)
a * d = 21
a * 9/c = 21
Multiply both sides by c
a * 9/c * c = 21 * c
a * 9 = 21 * c
9a = 21c ------ (5)
Make b the subject of formula in (1)
a + b = 8
b = 8 - a
Substitute 8 - a for b in (2)
b - c = 5
8 - a - c = 5
Collect like terms
-a - c = 5 - 8
-a - c = -3
Multiply both sides by -1
-1(-a - c) = -1 * -3
a + c = 3
Make a the subject of formula
a = 3 - c
Substitute 3 - c for a in (5)
9a = 21c becomes
9(3 - c) = 21c
Open bracket
27 - 9c = 21c
Collect like terms
27 = 21c + 9c
27 = 30c
Divide both sides by 30
27/30 = 30c/30
27/30 = c
0.9 = c
c = 0.9
Recall that a = 3 - c
So, a = 3 - 0.9
a = 2.1
From (1)
a + b = 8
2.1 + b = 8
b = 8 - 2.1
b = 5.9
From (3)
d * c = 9
Substitute 0.9 for c
d * 0.9 = 9
Divide both sides by 0.9
d * 0.9/0.9 = 9/0.9
d = 9/0.9
d = 10.
Hence, the solution to the box is
a = 2.1
b = 5.9
c = 0.9
d = 10
