Answer:
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
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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