solve the following algebra problem

Question

Write the slope-intercept form of the equation of the line passing through (3,2) and parallel too 2x - y = 5 

Answer 1

First you have to find the slope of the line 2x-y = 5.

 

You could do this by plugging in to random x variables to get points on the line, then using the rise over run calculation to determine the slope. Or we could rearrange the equation to this:

 

y = 2x-5   Which is the slope intercept form -> From here we can determine that the slope of the line is 2 

 

Now based on the definition of parallel we know that our equation must have a slope of 2, we just have to solve for the intercept using the point provided:

 

2 = 2(3) + b

 

b = -4

 

So the slope intercept from of this equation is:

 

y = 2x-4

 

Hope this helps

Answer 2

1) It's easiest to change the given equation into slope intercept form: y=2x-5

 

2) In order to make an equation that is parallel to the given one, it has to have the same slope. By putting the equation in slop intercept form, we can see that the slope is 2. So, we have to make sure that is the slope of our new equation.

 

3) y=mx+b is the slope intercept format. So, let's plug in the information that we have. Using the given point, plug in 3 for x and 2 for y. Then, plug in 2 for m, as m represents the slope of the equation: 2=2(3)+b.

 

4) Now, solve for b: 2=6+b --> 2-6=b --> b=-4

 

5) Now, just use this new information to form your equation! : y = 2x-4

 

y=2x-4 is your answer.