Question

the method of solving systems of equations by plotting them on a graph is known as the __________________ method.
the lines representing equations that overlap completely indicate that there are __________________ many solutions.
the slope-intercept form of a linear equation is represented as $y = mx + b$, where $m$ is the __________________ and $b$ is the y-intercept.

Explanation:

First Question:

In solving systems of equations, the graphical method involves plotting the equations on a coordinate plane and finding the intersection (or other relationships) to determine solutions. So the method of solving systems of equations by plotting them on a graph is the graphical method.

When two lines representing equations overlap completely, they are the same line, which means every point on the line is a solution. So there are infinitely many solutions.

In the slope - intercept form of a linear equation \(y = mx + b\), by definition, \(m\) represents the slope of the line (it describes the steepness and direction of the line), and \(b\) is the y - intercept (the point where the line crosses the y - axis).

Answer:

graphical

Second Question: