Equations and slopes

Question

write an equation of the line that passes through the point (-5,9) and parallel to 4x-2y=7

Answer 1

Hi Karla,

 

Here is one approach to the problem.

 

Let's use the point-slope approach to generate the equation.

 

We also need to remember that every line with the same slope is parallel so:

 

We first need to calculate the slope of the line by putting the second equation into slope intercept form by solving the equation for y.

 

We get 2y = 4x -7 or y = 2x - 7/2  Therefore the slope is 2

 

Now we use the point slope form y - y1 = m(x - x1)

 

y - 9 = 2(x - (-5)) 

 

simplifying the equation and putting it into slope-intercept form yields:

 

y = 2x + 19

 

Note that if we substitute -5 for x, the equation becomes 2*(-10)+19 which equals 9, so the equation works!

 

Hope this helps.

 

 

Answer 2

We first need to find the slope of the line that our new line is supposed to be parallel to. So we want to get that equation into the standard form of

 

y = mx + b

 

Starting with the given equation, we do a few operations

 

4x - 2y = 7

     +2y       +2y

4x        = 7 + 2y

      -7     -7        

4x - 7 = 2y

 

2x - 3.5 = y

 

So the slope, m, is 2. If our new line is supposed to be parallel to this one, how do the slopes of each line compare? They have to be the same.

 

Now we were given a point where our line is supposed to pass through. We know the slope, so we use the point-slope form of a line

 

(y - y1) = m * (x - x1)

 

Where (x1,y1) is our point and m is the slope.

 

(y - 9) = 2 * [x - (-5) ]

 

 

You can simplify this back to the standard form if you need to