Standard Form of Linear Equations - Problem 1
The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.
Here I have an equation that's given to us in slope intercept form. Slope intercept form is useful for graphing, but this problem wants us to turn it into standard from. It's really important that you're able to work between the three different forms of equations of lines.
So if I want to get this into standard form, that means I want it to look like some number times x, plus some number times y is equal to some constant. That's my goal. So I need to get both the xs, and ys on the same side on the equals. Then the regular old number which we call a constant should be by itself on the right hand side.
So let's see. This x needs to move over there. I'm going to subtract 2x from both sides, so now I have -2x plus y equals -4. Let's check and see if we have it. We have a coefficient times x, plus a coefficient times y. There isn't anything written there, but you can think of that coefficient as 1. I'm going to write it there in dashy lines. You don't have to write the 1, but it's implied that there is 1y, so that's okay. Then it's equal to my constant c. I'm all done.
That's an equation that's the exact same as that equation, only this one is written in standard form.