When two lines on a graph are parallel would it be infinite solutions

Answer 1

When two lines on a graph are parallel, they do not intersect at any point. This means that there are no solutions that satisfy both equations at the same time. Thus, parallel lines represent a scenario of zero solutions, not infinite solutions.

Conversely, if two lines are the same (which means they have all the same points), that situation would result in infinite solutions, as every point on one line is also a point on the other.

In summary:

• Parallel lines: Zero solutions
• Coincident lines (the same line): Infinite solutions

Answer 2

What if they have the same slope and y intercept?

Answer 3

If two lines have the same slope and the same y-intercept, they are identical lines (coincident). This means that every point on one line is also a point on the other line. In this case, the system of equations representing these two lines has infinite solutions, because there are infinitely many points (coordinates) that satisfy both equations simultaneously.

So, to summarize:

• If two lines have the same slope and the same y-intercept: Infinite solutions (they are the same line).
• If two lines have the same slope but different y-intercepts: Zero solutions (they are parallel lines).

Answer 4

Which number in an equation would be the "intercept"

Answer 5

In the context of linear equations, the term "intercept" commonly refers to two specific values: the y-intercept and the x-intercept.

1. Y-Intercept: This is the point where the line crosses the y-axis. In the slope-intercept form of a linear equation, which is given by: \[ y = mx + b \] here, \(b\) represents the y-intercept. It is the value of \(y\) when \(x = 0\).

2. X-Intercept: This is the point where the line crosses the x-axis. To find the x-intercept from the equation, you usually set \(y = 0\) and solve for \(x\). For a linear equation in standard form, \(Ax + By = C\), the x-intercept can be determined by rearranging the equation to find the value of \(x\) when \(y = 0\).

In summary:

• The y-intercept is represented by \(b\) in the equation \(y = mx + b\).
• The x-intercept is found by setting \(y = 0\) and solving for \(x\).