Parallel Lines in the Co-ordinate Plane:

 What is a Co-ordinate plane?

A coordinate plane is a fundamental concept of coordinate geometry, which describes a two-dimensional plane in terms of two perpendicular axes x and y along the horizontal and vertical direction of the plane.

What is a Slope?

The slant of a line on the coordinate plane is referred to as the slope. It is ratio of the change in the y-value to the change in the x-value, i.e.,

Slope = Change in y-value/Change in x-value

What is a Y-intercept?

The point where the line meets the y-axis is referred to as the Y-intercept.

What is the equation of a line?

The equation of a line, in co-ordinate geometry, can be written as:

Y = mx + c

Where m = slope and c = y-intercept

What is a negative slope?

If the slope m has a negative value, then it is referred to as negative slope.

What are the slopes of parallel lines?

Two non-vertical lines are parallel if and only if they have the same slope. (Two Vertical lines are parallel)

The slope can be determined using any of the following methods:

• Slope of a line
• Slope-intercept form
• Point-slope form

When a line is vertical it does not have a definite slope. So, therefore, vertical lines are parallel by definition. A line is said to be vertical if the x-coordinates of 2 points on the line are the same point.

When we want to define a line through a point parallel to a line, it can be done by using point-slope form. If we want to plot the line, we can do so by finding another point on the line using the equation of a line. Then, we can the line through the given 2 points.