Through (1,-6) parallel to the line x + 2y = 6

Hello!

To find the line parallel to the line x + 2y = 6 and passing through the point (1, -6), we will need to know that if two lines are parallel, then their slopes are equivalent to each other.

Since the given equation is written in standard form, we will need to change it to slope-intercept form to get the slope. Slope-intercept form is: y = mx + b.

x + 2y = 6 (subtract x from both sides)

2y = 6 - x (divide both sides by 2)

y = 6/2 - x/2

y = -1/2x + 3 | The slope of parallel lines are -1/2.

Since we are given the slope, we need to find the y-intercept of the line that goes through the point (1, -6) by substituting that point into a new equation with a slope of m equalling to -1/2.

y = -1/2x + b (substitute the given point)

-6 = -1/2(1) + b (simplify - multiply)

-6 = -1/2 + b (add 1/2 to both sides)

b = -11/2 | The y-intercept of the parallel line is -13/2.

Therefore, the line parallel to x + 2y = 6 and goes through the ordered pair (1, -6) is y = -1/2x + -11/2.