A line is parallel to x + 2y = -2 and intersects the point (6, 9). What is the equation of this parallel line?
1 answer:
Answer:
The equation of the parallel line is: y = -1/2x + 12
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given the line
writing into the slope-intercept form
dividing both sides by 2
comparing with the slope-intercept form y = mx+b
Thus, the slope m of the equation is: m = -1/2
We know that the parallel lines have the same slope.
Thus, the slope of a new line parallel to x + 2y = -2 is also: -1/2
Given that the line intersects the point (6, 9).
so substituting m = -1/2 and (6, 9) in the slope-intercept form to determine the y-intercept
y = mx+b
9 = -1/2(6) + b
9 = -3 + b
b = 9+3
b = 12
Thus, the y-intercept b = 12
now substituting b = 12 and m = -1/2 in the slope-intercept
y = mx+b
y = -1/2x + 12
Therefore, the equation of the parallel line is: y = -1/2x + 12
You might be interested in
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)