What is an equation of the line that is parallel to y=3x-8 and passes through the point (4,-5)

Question

I need an answer fast I don't understand how to do this 

Answer 1

Hello Savannah.

 

Two lines that are parallel MUST have the same slope.

 

The given line has slope M=3.

We know this because the equation of the line is:

    y = Mx + b

 

    y                = Mx +  b

    y = 3x  - 8  = 3x + -8

  

See how the bold numbers match up?!?!

 slope M matches 3 and intercept b matches -8

 

So the new line that is parallel MUST have slope 3.

It passes through (4 , -5)

 

As was just stated, the equation of any line is

  y = Mx + b

 

So the intercept b = y - M*x

Since it passes through (4, -5) 

that means when x=4 then it MUST be true 

that y=-5....  see?  (x=4, y = -5)

So when we plug in and substitute

x=4, y = -5, and M=3 into the equation

above in bold for b, the intercept b is:

  b = -5 - 3 * 4 = -5 - 12 = -5 + -12 = -17

 

So the equation of the new line that is parallel is:

  y = 3x + -17 = 3x - 17

 

It does pass through (4,-5) because when x=4

   y = 3(4) - 17 = 12 - 17 = -5.

It has slope 3, so it is parallel.

 

If you graph them, the original given line

crosses the y-axis at (0,-8). Then up three, one to the right.

Remember , slope M = 3 = 3/1 = rise/run .

Up 3, one to the right.

 

The new line that is parallel will cross the

y-axis at (0,-17) and passes through (4,-5).

Same slope, up three, one to the right.

 

Think of it like a staircase: adds 3 to y and 1 to x...

(0,-17)

(1,-14)

(2,-11)

(3,-8)

(4,-5)

Answer 2

It must have the same slope.

 

y = 3x + b

 

Use the given point to find b.

 

-5 = 3(4) + b

 

b = -17

 

y = 3x - 17