What is the relationship between the slope and the y-intercept to the systems of linear equation?

Slope and y-Intercept Values The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.

How are the slope and the y-intercept of the graph related to the equation?

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). This useful form of the line equation is sensibly named the “slope-intercept form”.

How does the slope-intercept form tell how many solutions a system of equations has?

Rewrite both equations in slope-intercept form. Compare the m- and b-values of the equations to determine the number of solutions. If the two equations have different m-values, then the system has one solution. If the two equations have the same m-value but different b-values, then the system has no solution.

How may solution’s do the system have if the slopes and y-intercepts are equal?

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. There are no points common to both lines; hence, there is no solution to the system.

How do you state the slope and y-intercept?

The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

What is the y-intercept and what does the y-intercept represent?

The y intercept is the point where the line crosses the y axis. If given the line in slope intercept form y = mx + b, the y-intercept would be the point (0,b), because the y-axis is at x = 0.

Can the slope and y-intercept be the same?

The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form. Use the slope to plot additional points.

How many solutions does the system have the solution to the system is?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Which is the system that has the same slope and different y intercept?

When lines have the same slope and different y-intercepts they are parallel lines. Parallel lines never intercept.

Which is the system that has the same slope and different y-intercepts?

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 do you already know about slopes and y-intercepts?

Summary. The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

When two linear equations have the same slope but different y-intercepts?

When a system of two linear equations have the same slope but different y-intercepts, they never meet in space. Since they never meet, there are no solutions. After graphing the fourth system, you can see that the lines are parallel. y = -2x + 1.

What is slope-intercept form?

For example, these are linear equations in slope-intercept form: [But this equation has x in the last term!] Slope-intercept is the most prominent form of linear equations. Let’s dig deeper to learn why this is so.

How do you find the y-intercept of a line?

The equation of any straight line, called a linear equation, can be written as: y = m x + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis. Homework Help | Algebra | Graphing Equations and Inequalities Email this page to a friend

How many times can two equations have the same slope?

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.