00:01
This problem wants us to find the general equation of a line, which is parallel to the line 3x minus 7y equal to 12 and passes through the 0 .64.
00:07
So what we need to do first is figure out the slope of this original line we're supposed to be parallel to because if it's parallel, we want the same slope.
00:15
So to do that, we'll isolate y to get this in the slope intercept form.
00:18
So that's negative 7y, and much we subtract 3x over, we'll get negative 3x plus 12.
00:24
And now when we divide by negative 7 for every term, that gets our original equation into slope intercept form.
00:30
Of 3 7th x minus 12 7th and the thing we care about is the 3 7th because in mx minus or excuse me mx plus b form here the slope is the value in front of your x so if we want our line that we're creating to be parallel we're going to keep the same slope so we know that we want our line to be y equals 3 7s x but we don't know what the y intercept of this line needs to be so we can use the point that is supposed to travel through as a sample x and y value to plug in so we can solve for b.
01:03
So when the y value is 4 equal to 3 7th times x and our x value is 6 that gives us the y value 4.
01:10
Now we have an equation again that only has one unknown so we can solve for it.
01:15
And when we multiply 3 7th times 6, that gives us 4 equal to 18 7th plus b.
01:22
And now we'll subtract 18 7th from both sides.
01:25
And we're trying to subtract 18 7ths from 4, so we need a common denominator of 7.
01:30
4 with denominator 7 is 28 7th equal to 187s plus b.
01:36
So when we subtract now the 18 7s from both sides, that's going to give us 10 7s.
01:46
So that's our b value that we needed...