A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Ro
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Answer:
(A) y - 7 = 2(x -2)
(B) y = -x + 6; y - 5 = -1(x + 1)
(C) Consistent independent
(D) (1, 5)
Step-by-step explanation:
(A) Road 1
(a) Slope
The <em>point-slope formula</em> for a straight line is
y₂ - y₁ = m(x₂ - x₁) Insert the points
3 - 7 = m(0 - 2)
-4 = m(-2) Divide each side by -2
m = -4/(-2) Divide numerator and denominator by-2,
m = 2
=====
(b) y-intercept
y₂ - y₁ = m(x₂ - x₁)
y₂ - 7 = 2(x₂ -2)
y - 7 = 2(x -2)
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(B) Road 2
(a) Slope
y = mx + b
Choose point (3,3)
m = (3 - 5)/(3 - 1)
m = -2/2
m = -1
=====
(b) y-intercept
y = mx +b
Choose point (3,3).
3 = -3 + b Add 3 to each side
b = 6
=====
(c) Equation of line (point-slope form)
y = mx + b
y = -x + 6
=====
(d) Equation of line (slope-intercept form)
y - 5 = -1(x - 1)
===============
(C) Consistency
The two roads intersect.
There is only one point of intersection, so this is a consistent, independent system of equations
===============
(D) Point of intersection
(1) y - 7 = 2(x - 2)
(2) y = -x + 6 Substitute (2) into (1)
-x + 6 – 7 = 2(x – 2) Remove parentheses
-x - 1 = 2x – 4 Add 4 to each side
-x +3 = 2x Add x to each side
3 = 3x Divide each side by 3
x = 1 Substitute into 2
=====
y = -1 + 6
y = 5
The point of intersection is (1, 5).
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