Gosh, where to start?
Welcome back to It All Adds Up! I’ve got quite a lot to cover… but i’m already busy enough with math! I am taking my very first midterm EVER- in fact, I have another It All Adds Up post scheduled for that date (which will most certainly be changed).
I wasn’t sure where to go with this episode, so I thought I would go simple but complicated. Hopefully, you already know about writing an equation in slope-intercept form, such as this example:
y value = slope * x value + y-intercept
Did I ever discuss how to find a y-intercept? Or an X-INTERCEPT? Probably not. What if i told you that there are also other ways to write an equation like this?
Let’s stick with slope-intercept form for a bit. We know how to find slope, and we know that the x value is how many times the slope will be multiplied by. For example, if ice cream cones cost $3.23 each, the mx would be y=3.23x. If he wanted to buy 2 ice cream cones, we would substitue in “2” for x and then we would be able to find the value of y. Algebra!
What about that ‘b’? That stands for the y-intercept. A y-intercept is the point on the y-axis where the line touches. This would be best represented by a rental company that charges a base charge in addition to a cost per __. The base charge is basically the amount with an x value of zero. Keep in mind that in order for an equation to be proportional, it must have a y-intercept of zero (starts at the origin [0,0]).
How do we find a y-intercept? All we have to do it substitute zero in for x in the equation and then solve for y. An x-intercept is the same thing, except that it is the value of x when y is zero, or when the line crosses the x-axis. An x-intercept can be found by substituting in zero for y and solving from there.
I’ve got plenty more to discuss, so click “Read More”!
X-intercepts are not found in slope-intercept form, but they are valuable in another. Let me introduce…
Standard form is just another way of writing y=mx + b. This form of an equation is most commonly used in situations like this:
You are selling tickets at a carnival. Tickets for children (x) are $5 each and tickets for adults (y) are $7 each. You sell $79 of tickets. How many of each type of ticket did you sell?
When an equation is written in standard form, it is basically a way of showing “if x is ___, then y is ___.” The way a standard form is written is:
ax + by = c
cost per x * x value + cost per y * y value = c
When solving an equation in standard form, you don’t normally substitute x and y, as you do not know these values. C would be substituted in for the total value that x and y equal. You solve this like any algebraic equation, this time for c. Let’s say that you had 10 adult tickets (y). You would substitute 10 for y and solve for how many x values there would be. Simple? For now.
What if you were asked to graph this equation? All you have to do is determine the x and y intercepts using the way above and plot both of those points on a graph. From there, you can connect the two points with a line.
Point Slope Form
Point slope form is yet another way to write an algebra equation. This equation is used when you are given an ordered pair and a slope-exactly what the name says.
y-y1 = m(x-x1)
This is certainly related to slope-intercept form. You substitute the slope for m, the x coordinate for x1 and the y1 coordinate for y. Once you do that, you can use the distributive property on the m(x-x1).
Think about it- this basically means that y minus the y coordinate (making y zero) equals the slope multiplied by the x coordinate plus the y-intercept. Seems a lot like slope-intercept right? Absolutely! You can easily convert this equation by adding the reciprocal of y1 to the right side’s y-intercept.
In order to graph this, you do have to convert to slope-intercept form, but it is easy to graph from there.
I know, this is complicated. And I know I didn’t do too well (at all) of explaining it. Maybe this will help a bit more: Quizlet. I have uploaded a small review set based on this episode of It All Adds Up, which can be reached by clicking on the Quizlet icon.
Thanks so much for reading!