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Find the slope of a line parallel to the graph of y 4x 2?
y = 4x + 2 Find the slope of a line parallel to the given equation. First, let's take a look at what it means to be parallel. The easiest way to look at it, is to think of railroad tracks. Parallel lines are the same distance apart for EVERY point on the line. This means, parallel lines will NEVER, ever cross. There will never be a point in common with both. Now think about how this will help us with our slope in the equation. Try to answer the following. Our parallel line will have: a) the same slope as the given line OR b) a different slope as the given line That's right, (a). If you're asked to find the equation/slope of a parallel line to a given line, the parallel line will always have the exact SAME slope as your given line! Since our given line y= 4x +2 has a slope of 4, the parallel line to y = 4x +2 will also have a slope of 4. Remember, the general form of a linear equation is y = mx +b, where m = slope and b = y-intercept.
How do you draw a line parallel to a given line?
[A Parallel line is a straight line, opposite to another, that do not intersect or meet.] Ie. Line 1 is Parallel to Line 2. ------------------------------------------------- <Line 1 ------------------------------------------------- <Line 2
How you would write the equation of a line given a point on the line and a parallel line?
y = 3x+5 is parallel to y = 3x+7
What is the locus of points at a given distance of a line?
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
Does a transversal line have to intersect with two parallel lines?
Yes, a transversal line always intersects two parallel lines.
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
Is a line parallel to itself?
Two lines are not parallel if they have exactly one point in common; otherwise they are parallel. So this means a line is parallel to itself!
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
Is it possible to construct a line that is parallel to any given line and that passes through a point that is not on the given line?
Yes. That's always possible, but there's only one of them.
Is y equals 5x plus 3 parallel or perpindicular?
Neither: because one line, by itself, can be neither parallel or perpendicular. These characteristics are relevant only in the context of another line (or lines). The given line is parallel to some lines and perpendicular to others.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
How do you identify the slope of the line that that would be parallel to the given line y5-3x?
Calculate the slope of the given line. Any line parallel to it will have the same slope.
How can you prove that a constructed line is parallel to a given line?
One way is to draw a straight line from the constructed line to the given line. If the lines are parallel, than the acute angle at the given and constructed line will be the same as will be the obtuse angles at the given and constructed line.
What is another name for the Playfair Axiom?
Another name for the Playfair Axiom is the Euclid's Parallel Postulate. It states that given a line and a point not on that line, there is exactly one line parallel to the given line passing through the given point.
How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
Through a given point on a given line there is exactly one line parallel to the given line what does it define?
Playfair Axiom
Find the slope of a line parallel to the graph of y 4x 2?
y = 4x + 2 Find the slope of a line parallel to the given equation. First, let's take a look at what it means to be parallel. The easiest way to look at it, is to think of railroad tracks. Parallel lines are the same distance apart for EVERY point on the line. This means, parallel lines will NEVER, ever cross. There will never be a point in common with both. Now think about how this will help us with our slope in the equation. Try to answer the following. Our parallel line will have: a) the same slope as the given line OR b) a different slope as the given line That's right, (a). If you're asked to find the equation/slope of a parallel line to a given line, the parallel line will always have the exact SAME slope as your given line! Since our given line y= 4x +2 has a slope of 4, the parallel line to y = 4x +2 will also have a slope of 4. Remember, the general form of a linear equation is y = mx +b, where m = slope and b = y-intercept.
