Question

For each function, determine if it intersects or is parallel to the line y = -1.5x. If it

Answer 1

Answer:

y=0.5x+4 intersects y=-1.5x.

The intersection point is (-2,3)

Step-by-step explanation:

First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.

So we have the equation:

$y=-1.5x$

Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5

The equation given to us is:

$y=0.5x+4$

As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.

To find the x-value of their intersection, simply set the equations equal to each other and solve for x.

$-1.5x=0.5x+4\\-2x=4\\x=-2$

Now, plug -4 into either of the equations:

$y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3$

Therefore, the point of intersection is (2,3).

Answer 2

Answer:

Intersects; intersection point: (-2,3)

Step-by-step explanation:

Substitute -1.5x for y into y=0.5x+4:

-1.5x = 0.5x +4

-1.5x - 4 = 0.5x

-4 = 2x

x = -2

Plug in -2 for x into y=-1.5x

y = -1.5(-2)

y = 3

Organize the x and y values into an ordered pair:

(-2,3)