(3,12);y= -1/4x+7

Question

Write an equation in slope intercept form of the line that passes through th given point and is parallel to the graph of the given equation

Answer 1

Parallel lines have the same slope, so the slope of the new line will be -1/4.  All you have to do is substutute 3 and 12 for x and y, and solve for the intercept b.

y = -1/4 x + 7

12 = -1/4 (3) + b

12 = -3/4 + b

12 3/4 = b

y = -1/4 x + 12 3/4

 

Answer 2

You are looking to find an equation, in slope-intercept form, of the line that passes through the point (3, 12) and that is also parallel to the line whose equation is  y = (-1/4)x + 7. 

First, recall that the slope-intercept form of a linear equation is as follows:

     y = mx + b ,  where 'm' represent the slope of the line and 'b' represents the y-intercept of the line. 

Also, recall that for any two individual lines to be parallel to one another they must have the same slope. 

With this, we know that the line in question must not only pass through the point (3, 12), but must also have a slope of -1/4.

Therefore, we are given the following:     x = 3  ,     y = 12  ,  and     m = -1/4 

Plugging in these numbers into the slope-intercept form of a linear equation, y = mx + b, we can solve for the unknown variable, b, to yield the linear equation in question.

        y = mx + b

      12 = (-1/4)(3) + b

      12 =  -3/4  +  b

Solve for 'b' by adding 3/4 to both sides of the equation:

     12  +  3/4  =  -3/4  +  3/4  +  b

     12  +  3/4  =  0  +  b

In order to add 12 to 3/4, both numbers must possess a common denominator. In this case, the least common denominator is 4, and so we have to convert 12 to fraction with a denominator of 4 by multiplying  it by 4/4 to yield 48/4 (i.e., 12*(4/4) = (12/1)*(4/4) = (12*4)/(1*4) = 48/4): 

     12  +  3/4  =  b

     48/4  +  3/4  =  b

     51/4 = b

Now that we have found 'b' and we know 'm', we arrive at the following:

           y = mx + b

          y = (-1/4)x + 51/4