Can two lines have the same y-intercept but different slopes?
If 2 lines have the same y-intercept but different slopes, what can you conclude? Psykolord1989 . If two lines have different slopes, they cannot be the same line. However, if they share a y-intercept, that means they cross the y -axis at the same y value.
How do you know if two equations have the same slope?
Log in here. If two equations have the same slope and the same y-intercept, then they are the same line, therefore meaning that they connect an infinite number of times on the graph. These lines have an infinite number of solutions, meaning that the same numerical values one uses for x and y in the first solution will also work for the second.
What does it mean when two variables share a y-intercept?
However, if they share a y-intercept, that means they cross the y -axis at the same y value. Since the x value is constant on the y-axis (0), they also share an x-value here.
What is the equation for Y in terms of X?
The equation is as follows: y=mx+b where "m" serves as the slope and "b" serves as the y-intercept. In some textbooks this is also called solving for y in terms of x.
What does it mean if two equations have the same slope and different y-intercepts?
These two equations have the same slope, but different y-intercepts. That means that they are moving in the same direction and doing the same thing, but at different locations. These lines are parallel. This system is an inconsistent system, because these lines are parallel and have no solution.
Can a one solution have the same y-intercept?
Solutions of systems of linear equations: infinitely many solutions. A system of linear equations has infinitely many solutions if the lines have the same slope and the same y-intercept.
What if two linear equations have the same slope?
Parallel lines are lines that will go on and on forever without ever intersecting. This is because they have the same slope! If you have two linear equations that have the same slope but different y-intercepts, then those lines are parallel to one another!
Which two lines have the same y-intercept?
Two lines with the same y-intercept are perpendicular.
What does it mean when two lines have the same slope?
parallelIf lines are parallel, they slant in exactly the same direction. If they are nonvertical, their steepness is exactly the same. Theorem 103: If two nonvertical lines are parallel, then they have the same slope.
What can you say about two lines that have equal slopes and equal y-intercepts?
Solution. They are the same line. The slope and y-intercept uniquely define a line.
How do you know if two equations are parallel?
0:093:59How To Tell If Two Lines Are Parallel, Perpendicular, or Neither? - YouTubeYouTubeStart of suggested clipEnd of suggested clipHow can you tell if these two equations are parallel perpendicular or neither. The key is the slope.MoreHow can you tell if these two equations are parallel perpendicular or neither. The key is the slope. The slope for both functions is equal to 5..
Does the relationship of the y intercepts of perpendicular lines matter?
Correct answer: For two lines to be perpendicular, their slopes have to have a product of . Find the slopes by the coefficient in front of the . and so the two lines are perpendicular. The y-intercept does not matter for determine perpendicularity.
How are the y intercepts of parallel lines related?
1 Expert Answer While parallel lines have the same slope they have different y-intercepts. If the y-intercepts were the same the lines would be collinear.
How do you find the equation of a parallel line with the same y-intercept?
1:362:30Finding a line parallel to another line given the y intercept - YouTubeYouTubeStart of suggested clipEnd of suggested clipGo ahead and see that the answer is just going to be y equals 9x minus 2. B is your y intercept. YesMoreGo ahead and see that the answer is just going to be y equals 9x minus 2. B is your y intercept. Yes. Exactly because remember three is for this equation. Right and for this.
What does coincident mean in math?
The word 'coincide' means that it happens at the same time. In Mathematics, coincidence is defined as the lines that lie upon each other. It is placed in such a way that when we look at them, they appear to be a single line, instead of double or multiple lines.
Does the y-intercept matter in parallel lines?
Parallel lines must have unequal y-intercepts because otherwise the lines would be identical, in which case they would not be parallel but one and the same. The y-intercept is where a line crosses the y-axis, which is when x = 0. If two lines are parallel, then they never intersect.
When two equations have the same slope and y-intercept how many solutions exist?
2 Answers By Expert Tutors You get infinite solutions if two lines have the same slope and the same y intercept (y = (5/4)x+1 and y = (5/4)x+1). You get no solutions if two lines have the same slope and different y-intercepts (y = 2x+1 and y = 2x -3).
Do lines with the same slope intersect?
If the two lines do not have exactly the same slope, the lines will eventually intersect, but if the slopes are the same (and the y-intercepts are different), they will never intersect. Suppose two lines have the same slope: y = 2x + a and y = 2x + b.
What qualifies as no solution?
The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
How do you tell if a system of equations has no solution or infinitely many?
A linear system has many (infinite) solutions when the two lines are the same (such as y=x+3 and 2y=2x+6 ). And a linear system has no solution when the lines never intersect (in other words, they're parallel; their slopes are equal).
How many times does a line intersect?from algebra.com
always two line will intersect only once.
Where is the intersection of a graph?from algebra.com
as can be seen on the graph, their only point of intersection is at the y intercept.
Why are lines perpendicular?from algebra.com
these lines are perpendicular because their slopes are negative reciprocals of each other. as can be seen on the graph, their only point of intersection is at the y intercept.