Week 15 of Math 10 and Week 4 of quarantined classes. This week has been fairly quiet, nothing absolutely massive or no new revelations, which is nice considering how this quarantine makes lessons harder. In this blog post I will be covering Parallel and Perpendicular lines, a topic that I was unable to add into my previous blog post, alongside Linear functions.

Parallel and Perpendicular lines are types of lines that are adjacent or directly on a certain line. Parallel lines are lines that will never intersect with the main line.

In this image, the blue line is our main line while the green line is it’s parallel. Notice how both lines have the exact same slope but are situated on different parts of the y-axis. The slope of the first line is always equal to that of the second line if it’s a pair of parallel lines.

Perpendicular lines on the other hand are the complete opposite. These lines will always intersect with the main line no matter what.

Here, you can see that the red line intersects with the main blue line,. The slope of the main line is 2 or while the slope of the red line is -0.5 or . If you had a keen eye you’d notice that the slopes for both lines are polar opposites, or in math terms, negative reciprocals of each other. So in order to find the slope of a perpendicular line you have to flip the slope of the main line on it’s head then turn it into a negative. Another note is that since these lines are negative reciprocals, they will always result in -1. multiplied by is equal to or -1.

So if you were given two different slopes e.g and 2x, this is how you’d solve for both parallel and perpendicular lines.

If you’re looking for a parallel line, you know that the slope of the first line is equal to the slope of the second line, or = . Your goal is to isolate x, so plug in the values then follow the order of operations.

If you’re looking for a perpendicular line, then the formula for finding it is because perpendicular lines are always =-1. So plug in the values then follow the order of operations like above.

Next in line are Parent Functions. Parent functions are lines that are the base version of all functions. They have a slope of 1, have both an x and y intercept of (0,0) and are written as y=x. This is how they look like on a graph.

If other numbers are added to the Parent function they become something else entirely. In this case they can become linear functions which are written using the slope y-intercept form, or y=mx+b. M refers to the slope while B refers to the y-intercept. When it comes to solving equations the value you’re looking for may vary, but its all a matter of what information is given to you. Here, I’m going to provide three different questions and the methods to approach them.

M = -2, passing through (3,6). For this question we already have the slope given to us but we don’t know how the values for x, b and y. Luckily, since coordinates are formatted as (x,y) we know that the values for x and y are 3 and 6 respectively. Plug in the numbers then follow the order of operations.

The answer comes to y=-2x+12.

Goes through (8, 6) (4, 3). For this question, we aren’t given anything except two coordinates, but while this may seem impossible to do, remember to always try to find the slope first. In order to find the slope, use the slope formula .

Now that we know the slope is we can make the slope interval equation y=x+b. The next step is to choose a coordinate to plug in the values, then follow algebra. It actually doesn’t matter which coordinate you choose, both will share the same answer.

Since B=0 the answer just ends up being  y=.

Perpendicular to y=+4 going through (8,2). Now perpendicular and parallel are coming into play. Since the question says perpendicular, we have to flip to become or 4, but there are two different y-intercepts that are shown. The +4 in the slope interval and the 2 in the coordinate, so which one do we plug into the equation? The answer is always the coordinate, meaning that even if the coordinate were replaced with “y-intercept of 2” you still use 2 because a y-intercept of 2 is just (0,2). Plug in the numbers then algebra takes over.

And you’re done!

The sooner you take it, the more effective it will be. viagra 100mg Myth 2: Pharmacists simply choose not to sell ECPs to people other than the woman taking the medication a partner or family member, for example.