the slope-intercept form of the line passing through the point (3,-6) and parallel to the line y=-4x+3

Question

how do you do this? i need help, a lot of help bc i don't know how to do this omg 

Answer 1

Hello, 

Glad to answer your question. 

Let's break up the problem. There are two given information about the line, which are as below.

 

Given:

(i) the coordinate of the point that the line goes through is (3,-6)

(ii) the slope of the parallel line is -4.  

 

 

First, we can have the slope of the line by using information (ii), because all parallel lines have the same slope.  So the slope of the line is -4. 

 

Second, we know that the slope-intercept formula when we know the coordinate of a point on the line as (x₁, y₁) and the slope as m.  Then the formulas is given as below. 

 

y-y₁ = m(x-x₁)          .....................(1)

 

Because we now know the coordinate of a point on the lline and the slope, we can plug in the values to the equation (1).  Then, what we have is

 

y-(-6) = (-4)*(x-3)    ....................(2)

 

Then, we arrange the equation as follows by using distribution property etc.

 

y+6 = -4x+12

 

Subtracting 6 from both hand side of the equation,

 

y = -4x + 6

 

Therefore, the answer is:

 

y = -4x + 6       ........................(3)

 

[check the answer]

We can check if the answer is correct.  Plug in the given coordinate into equation (3),

(3,-6) into equation (3)

Then, -6 = -4*3 +6

         -6 = -12 +6

         -6 = -6

So, our answer is correct. 

 

 

 

Answer 2

Hey Fatima -- since parallel lines never cross, they must have the same slope -4 ...

 

y= -4x +b ... plug in point (3,-6) to find "b" ... -6 = -4(3) +b ... b= 6 ...

 

y= -4x +6 ... RECAP: keep same sloping for parallel lines, plug in test point to get "b"