Answer:
y = - 12x - 47
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 = - 12x - 2 ← is in slope- intercept form
with slope m = - 12
Parallel lines have equal slopes, thus
y = - 12x + c ← is the partial equation
To find c substitute (- 4, 1 ) into the partial equation
1 = 48 + c ⇒ c = 1 - 48 = - 47
y = - 12x - 47 ← equation of parallel line
The required equation of the line is y = -12x - 47
"The equation of the line having slope m and passing through points (p, q) is (y - q) = m(x - p)"
"y = mx + c, where m is the slope and c is the Y-intercept of the line."
For given question,
We have been given a point (-4, 1)
The required line is parallel to the line y = -12x - 2
Comparing above equation with slop-intercept form of the line.
m = -12
Let m1 be the slope of the required line.
We know that the slope of parallel lines is equal.
⇒ m1 = m
⇒ m1 = -12
Now we find the equation of the required line by using slope-point form.
Let (p, q) = (-4, 1)
By using slope-point form,
⇒ (y - q) = m1(x - p)
⇒ (y - 1) = -12(x - (-4))
⇒ y - 1 = -12x - 48
⇒ y = -12x - 47
Therefore, the required equation of the line is y = -12x - 47
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