5x+8y=120 line passes 4,5 find parallel
1 answer:
5x + 8y = 60
the equation of a line in ' slope-intercept form ' is
y = mx + c → (m is the slope and c the y-intercept)
rearrange 5x + 8y = 120 into this form
subtract 5x from both sides
8y = - 5x + 120
divide all terms by 8
y = - x + 15 ( in slope-intercept form)
hence slope m = -
Parallel lines have equal slopes
thus partial equation is
y = - x + c
to find c substitute (4, 5) into the partial equation
5 = - + c ⇒ c =
y = - x +
multiply through by 8
8y = - 5x + 60 ⇔ 5x + 8y = 60 → (equation of parallel line)
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Answer:
<h3>Postulates and Theorems</h3>A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates.
Postulate 1: A line contains at least two points.
Postulate 2: A plane contains at least three noncollinear points.
Postulate 3: Through any two points, there is exactly one line.
Postulate 4: Through any three noncollinear points, there is exactly one plane.
Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.
Postulate 6: If two planes intersect, then their intersection is a line.
Theorem 1: If two lines intersect, then they intersect in exactly one point.
Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point.
Theorem 3: If two lines intersect, then exactly one plane contains both lines.
Example 1: State the postulate or theorem you would use to justify the statement made about each figure.
(a)
Through any three noncollinear points, there is exactly one plane (Postulate 4).
(b)
Through any two points, there is exactly one line (Postulate 3).
(c)
If two points lie in a plane, then the line joining them lies in that plane (Postulate 5).
(d)
If two planes intersect, then their intersection is a line (Postulate 6).
(e)
A line contains at least two points (Postulate 1).
(f)
If two lines intersect, then exactly one plane contains both lines (Theorem 3).
(g)
If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2).
(h)
If two lines intersect, then they intersect in exactly one point (Theorem 1).
