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