Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?

Question

may you please help me out with this problem..

Answer 1

First you need to understand the slope-intercept form

 

y = mx +b

 

m = the slope of the line

b = the y-axis intercept

 

y and x represent the coordinates of a point on the line

 

So for the equation that you listed we know that the slope, m , is (3/4).  We also know a given point on the line.  therefore we also have a y value (1/3) and a x value (4).

 

So plug in the numbers:

 

(1/3)=(3/4)*4 + b

 

So to find the equation of this line we must solve for b

 

Multiply (3/4) and 4 to get 3

 

(1/3) = 3 + b

 

Now subtract 3 from both sides in order to isolate b

 

-2 2/3 = b or -8/3 = b

 

Now rewrite the equation with the y-intercept, b.

 

y = (3/4)x - (8/3)

 

From the wording I am assuming you are given a list of equations to chose from.  It is possible that the some of all of the equations are listed in standard form.  In that case, we need to find the equation:

 

Ax + By = C

 

To do that we simply take the slope intercept equation and manipulate it algebraically  

 

y = (3/4)x - (8/3)  First subtract (3/4)x from both sides

 

-(3/4)x + y = -(8/3)  This is technically standard form but we can clean it up a bit by multiplying both sides of the                                          equation by -4.

 

So -4 * -(3/4)x = 3x

     -4 *y = -4y

    -4 *-(8/3) = 32/3

 

So 3x - 4y = 32/3

 

I hope this helps