Find the equation of a line that runs through
(-6,2) and is parallel to a line with a slope of -1/4

The equation of a line that runs through  (-6,2) and is parallel to a line with a slope of (-1/4)     is  x + 4y  - 2 = 0

Step-by-step explanation:

Slope of the parallel  equation is m 1 = (-1/4)

If the two liner are parallel the, slope of both lines are equal.

⇒The slope of the equation of line = m2  = m1  = -(1/4)

The point (x0, y0)  = (-6,2)

Now, by THE POINT SLOPE FORMULA:  The equation of a line is given as

( y - y0)  =  m (x -x0)

Now, here the equation of line is given as:

or, 4y - 8 + x + 6 = 0

or, x + 4y  - 2 = 0

Hence, the required line equation is  x + 4y  - 2 = 0

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step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)