Write the equation of a line parallel to y = 2x - 3.

Question

My question is mostly about slopes

Answer 1

Hello, thank you for taking the time to post your question!

The equation of a line parallel to y=2x−3 will have the same slope, which is 2.

The general equation for any line parallel to it is y=2x+b, where b can be any number.

For example, y=2x+10 is an equation of a line parallel to the given line.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Christina,

 

This is a very important question to understand. You should be familiar with the slope/intercept form for linear equations, y = mx + b. When we write a linear equation in the form y = mx + b, it is very easy to get a mental picture of the line: m represents the slope of the line, and b is the y-intercept.

 

So for your example of y = 2x - 3, the line has a slope of +2 and has a y-intercept of -3. To graph this line start at the point (0,-3,) which is the y-intercept, and then use the slope of 2 to draw the line. "Go up 2, over 1, go up 2, over 1." Keeping in mind that slope is just "rise / run."

Two lines are parallel if they have the same slope, but are not the same line. There are, in fact, infinitely many lines that are parallel to y = 2x - 3. Here are a few examples:

 

• y = 2x
• y = 2x + 3
• y = 2x - 17
• y = 2x + 40
• y = 2x + 1,000,000,000,000,000,000,000,000

 

Just make sure not to answer with "y = 2x - 3", as lines are not considered parallel to themselves. Kind of a technicality, but it's important to make sure you get a correct answer. 

 

Hope this helps!