Write an equation parallel to y=2x+4 that passes through the point -4,-1

The required equation of the line parallel to y=2x+4 that passes through the point (-4,-1) is y = 2x + 7

The equation of a line in point-slope form is expressed as:

Given the equation y = 2x + 4

mx = 2x

m = 2

Given the point (x0, y0) = (-4, -1)

Substitute the point and the slope in the given equation above;

y - (-1) = 2(x-(-4))

y+1 = 2(x+4)

y + 1=  2x + 8

y = 2x + 8 - 1

y = 2x + 7

Hence the required equation of the line parallel to y=2x+4 that passes through the point (-4,-1) is y = 2x + 7

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y = 2x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 4 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (- 4, - 1) into the partial equation

- 1 = - 8 + c ⇒ c = - 1 + 8 = 7

y = 2x + 7 ← equation of parallel line

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let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!