First of all, the equations above are in slope-intercept form. Two lines that are parallel have the same slope, and two lines that have the same slope are parallel. (Similarly, two lines that have slopes that multiply to minus 1 are perpendicular.)y=2x+1
y=2x+2
we are supposed to find out if these two are parallel, or hit at one point etc.
i plugged in 0 to y and x separately in each and got
(0,2),(-1,0); (-1/2,0)
And put them on a graph. Couldn't tell if they were parallel but they looked it so I did
m= (y2-y1)/(x2-x1) for each and got a slope of 2 and a slope of 1/2
maybe i did something wrong...
You should show how you calculated the slopes (even though you did not need to in this case) because otherwise we cannot explain why you went wrong.y=2x+1
y=2x+2
from inspection now I notice the 2 stands for the slope.
First of all, the equations above are in slope-intercept form.
Two lines that are parallel have the same slope, \(\displaystyle \ \ \ \ \)or each line has no slope.
and two lines that have the same slope are parallel. \(\displaystyle \ \ \ \ \)That is not necessarily true.*
(Similarly, two lines that have slopes that multiply to minus 1 are perpendicular.) \(\displaystyle \ \ \ \ \)**
* For example, the lines y = 2x and 3y = 6x have the same slope, but they are not parallel lines. They are the same line.
** Also, a line with a zero slope and a line with an undefined slope are perpendicular to each other.
Not in any axiomatic geometry I have ever seen! For example, Wikipedia says "In geometry, parallel lines are lines in a plane which do not meet. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not intersect or touch at any point are said to be parallel."It is worth noting that any line in \(\displaystyle \Re^2 \) is parallel to itself. That is the standard definition in axiomatic geometry.
Moreover \(\displaystyle y=2x~\&~3y=6x \) are two expressions that represen one line.
Any two vertical lines are parallel.
If \(\displaystyle \ell_1~\&~\ell_2 \) are two lines with slopes \(\displaystyle m_1~\&~m_2 \) are their slopes then if \(\displaystyle {\ell _1} \bot {\ell _2}\text{ if and only if }\) one in vertical and one horizontal or else \(\displaystyle m_1\cdot m_2=-1 \).
Not in any axiomatic geometry I have ever seen! For example, Wikipedia says "In geometry, parallel lines are lines in a plane which do not meet. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not intersect or touch at any point are said to be parallel." "oracle" says "Parallel lines are coplanar lines that do not intersect."