Table of Contents
What does it mean if two equations have the same y-intercept?
If the y-intercepts are the same, the two equations represent the same line and there are INFINITELY MANY SOLUTIONS. 3b. If the y-intercepts are different, the two equations are distinct parallel lines and have NO SOLUTION.
What is it called when two lines have different slopes?
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
Which two lines have the same y-intercept?
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system.
Can two different lines have the same slope?
In other words, the slopes of parallel lines are equal. Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.
What does it mean if the slopes are different?
The two lines in the graph below are parallel lines: they will never intersect. Notice that they have exactly the same steepness which means their slopes are identical. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel.
What are inconsistent systems?
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Do coinciding lines have the same y-intercept?
The coinciding lines are identical lines that fall exactly on top of one another and cut the respective axis on the same points. So, all the coinciding lines have the same intercept, whether on the x-axis or the y-axis.
What are the different slopes?
From the previous section, you have discovered that there are four types of slope.
- postive slope (when lines go uphill from left to right)
- negative slope (when lines go downhill from left to right)
- zero slope (when lines are horizontal)
- undefined slope (when lines are vertical)
When two linear equations are solved for Y and the slopes are different and the y-intercepts are different?
Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of two parallel lines will have NO solution (no intersection of the lines.)
How is slope different from a y-intercept?
The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis. The slope and the intercept define the linear relationship between two variables, and can be used to estimate an average rate of change. The y-intercept is 2. The slope is negative 0.4.
How do slopes and y intercepts of two equations compare?
how do the slopes and y intercepts of the two equations compare? In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis).
When do two lines have the same y intercept?
You can put this solution on YOUR website! always two line will intersect only once. if they have the same y intercepts then that is their point of intersection.
What happens when two linear equations have the same slope?
If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of two parallel lines will have NO solution (no intersection of the lines.) 2. Can a linear system with infinitely many solutions to contain two lines with different y intercepts?
Why are the lines of Y perpendicular to each other?
y = 1/2x + 3. —–. 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.