parallel to y=-7-3 passes through point (2-5)

Question

find a line that is paralle ly = -7x-3, and passes through the point (2,-5) graph both lines on the graph

Answer 1

Hi Destra;

y = -7x-3

The equation is in the format of...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

The slope of this equation is -7.

The slope of any equation parallel to it is -7.

(The slope of any equation perpendicular to it is 1/7.  But that is another Wyzant answer.)

We could proceed using the slope-intercept formula...

y=-7x+b

Plug in...

-5=[(-7)(2)]+b

-5=-14+b

Let's add 14 to both sides...

14-5=-14+b+14

9=b

The formula is...

y=-7x+9

 

We could also proceed using the point-slope formula...

y-y₁=m(x-x₁)

y--5=-7(x-2)

Subtracting a negative number is the same as adding a positive number.

y+5=-7x+14

Let's subtract 5 from both sides...

-5+y+5=-7x+14-5

y=-7x+9

Answer 2

Hi, Destra

 

You have the line y = -7x - 3

 

A line parallel to it will have the same slope, namely -7.

 

We also know that the point (2, -5) lies on this parallel line.

 

y = -7x + b

 

-5 = -7*(2) + b

 

-5 = -14 + b

 

b = -5 - (-14) = 9

 

So the equation of our line is

 

y = -7x + 9.

 

It has the same slope as the original line, but a different y-intercept.