What type of solution does a system of linear equations have if the slopes and Y intercept are the same?
A system of linear equations has infinitely many solutions if the lines have the same slope and the same y-intercept.
What is the graph you expect to see when the linear functions within a system have the same slope?
Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel.
What does it mean if two equations have the same slope but different y-intercepts?
parallel lines
When lines have the same slope and different y-intercepts they are parallel lines. Parallel lines never intercept. Because these lines never intercept, they have no solution.
What are the equations of the 2 lines in slope-intercept form?
Step 3: Write the equation in slope-intercept form (y = mx + b) At this point, you’ve solved for both m and b. All that’s left to do is to plug them both in and write the equation in slope-intercept form (y = mx + b).
How many solutions does a linear equation in two variables have if the slopes of the lines are equal and the y-intercepts are also equal?
There are infinitely many solutions to this system. If you write the second equation in slope-intercept form, you may recognize that the equations have the same slope and same y-intercept. Solve the system by graphing: {y=−3x−66x+2y=−12.
How can you tell if two linear equations make a dependent system just by looking at the slope-intercept form of their equations?
If the slopes and intercepts are the same, then they must be the same line. The first equation in our previous example was in the form y = mx + b, also called slope-intercept form. This tells us that they are the same line and that the system of equations is dependent.
How do you graph two linear equations?
Graph a linear equation using the intercepts.
- Find the x– and y-intercepts of the line. Let. and solve for x. Let. and solve for y.
- Find a third solution to the equation.
- Plot the three points and check that they line up.
- Draw the line.
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 happens when the slopes are the same?
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.
How do u write an equation in slope-intercept form?
The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It’s usually easy to graph a line using y=mx+b.