# *Showing that two lines are coincident - Help please.

• nukeman
In summary, the problem is asking to show that two lines, L and M, are coincident. To do this, we must write the equations for both lines in slope-intercept form, which is y = mx + b. By doing this, we can see that both lines have a slope of 2 and a y-intercept of -5. This means that the lines have the same slope and y-intercept, making them coincident. The confusion may have stemmed from the mistake in stating the y-intercept as (0,5) instead of (-5). The slope-intercept form of the equation of a line contains the slope and the y-intercept.
nukeman

## Homework Statement

First off, this is a homework question, but an example so answer is given. need help understanding it.

-Show that ht elines given by the equations below are coincident:
L: 2x - y = 5
M: -4x + 2y = -10

Solution: Write each equation in slope-intercept form:

L: 2x - y = 5
-y = -2x + 5
y = 2x - 5

M: -4x + 2y = -10
2y = 4x - 10
y = 2x - 5

Answer: The lines L and M have a slope of 2, and the same y intercept (0,5) so they are coincident.

I don't understand how they got that answer of slope of 2 and y intercept of (0,5)

?

Thanks everyone!

nukeman said:

## Homework Statement

First off, this is a homework question, but an example so answer is given. need help understanding it.

-Show that ht elines given by the equations below are coincident:
L: 2x - y = 5
M: -4x + 2y = -10

Solution: Write each equation in slope-intercept form:

L: 2x - y = 5
-y = -2x + 5
y = 2x - 5

M: -4x + 2y = -10
2y = 4x - 10
y = 2x - 5

Answer: The lines L and M have a slope of 2, and the same y intercept (0,5) so they are coincident.
The y-intercept for these lines is NOT at (0, 5). Check your book again to see what it says.
nukeman said:
I don't understand how they got that answer of slope of 2 and y intercept of (0,5)

There are several forms of the equation of a line.
What is the slope-intercept form?
What information does the slope-intercept form of the equation of a line contain?

## 1. How can I prove that two lines are coincident?

To prove that two lines are coincident, you need to show that they have the same slope and y-intercept. This can be done by finding the equations of the two lines and comparing them. If the equations are identical, then the lines are coincident.

## 2. What is the difference between coincident lines and parallel lines?

Coincident lines are lines that lie on top of each other and have the same equation. Parallel lines, on the other hand, have the same slope but different y-intercepts. This means that they will never intersect.

## 3. Can two lines be coincident if they have different equations?

No, two lines must have the same equation to be coincident. This means that they must have the same slope and y-intercept. If the equations are different, then the lines are not coincident.

## 4. Are coincident lines the same as identical lines?

Yes, coincident lines and identical lines refer to the same concept. They both mean that two lines have the same equation and lie on top of each other.

## 5. How do I write the equation of a coincident line?

The equation of a coincident line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Since coincident lines have the same equation, you can use the equation of either line to represent both lines.

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