# Equivalent Equations: Standard Form vs Slope-Intercept Form This tutorial is a very quick
introduction to equivalent equations. We’re going to be dealing with Standard
Form versus Slope-Intercept Form of linear equations in standard form, and
slope-intercept form, both have their uses. Let’s say we were given an example; three burgers and two fries cost a total of \$8, well which would be better Standard Form that’s Ax plus By equals C and Slope- intercept form Y equals MX plus B., It would be Standard Form, three burgers plus two fries equals eight dollars, it just goes straight into Standard form, you just make the B and F into X and Y, but we want to make that Slope-intercept Form so you got to move the three X to the other side and then divide both sides by the two to get Y all by itself, you also need to switch those around that minus three X becomes negative three X positive eight becomes plus eight and when you divide everything by two, you’re going to get that in Slope intercept form y equals negative 3 over 2x plus 4 now. I’ll do another example, be much slower than that I’ll take my time but that’s what’s going on those are equivalent equations, you have standard form and you have slope intercept, form standard was easier to write, but slope-intercept form is easier to graph, you start at the 4 and you’re gonna go down 3 over 2 down 3 over 2, down 3 over 2 nice and easy to graph, but let’s go ahead and look at another example, now are these two equivalent? 14x plus 7y equals 21, and the Y equals negative 2x plus 3, well let’s see let’s do what we did before and try to solve for Y or first going to move that 14x to the other side like we did before, it’s taken nice and easy we’re going to go minus 14x and minus 14x so we’re left with 7y on the left side and we have 21 minus 14x on the other side, remember they’re not like terms you just leave them like that and remember that’s a positive 21. I’m gonna switch those around in a second and we still have 7y, and it’s going to be negative 14x and a positive 21, now it’s starting to look more like slope-intercept form over there we divide all of our terms by the 7, so we can get that Y by itself divide everything by 7 and finally we get Y is equal to a negative 2x plus 3 so, you see are those equivalent yes they are, they’re exactly the same. So let’s look at another example
are these two going to be equivalent? 4x plus 6y equals 18, and Y equals 2/3x
plus 3, again we’re going to take that 4x move it to the other side because we’re
going to solve for Y we subtract out the 4x and notice we have a positive 18 and a negative 4x, we’re gonna go ahead and skip a step we write 6y equals and then just bring down the negative 4x and the positive 18 we’re getting quicker at this now again we’re going to divide everything
by 6 divided by 6, divided by 6, divided by 6 six, five by six is one. Now we need to simplify this fraction two goes into four and six divide them both by two, we’re gonna get negative two and a positive 3x and a positive 18 divided by 6 is 3, are these equivalent. Let’s see we have a negative 2/3x our slope is negative 2/3, over here it’s a positive 2/3, and it was a trick question; no these two are not equivalent so again this is just a brief introduction to equivalent equations, you try to set them up so that they look exactly the same, and if they’re not of course they’re not going to be equivalent and again Standard Form and Slope-intercept form are going to be very common on any test you see, so make sure you understand how to make them look the same.