A 3 1 and b2 2 are two points on a straight line i find the...

a(-3, 1) and b(2, -2) are two points on a straight line. (i) Find the equation of the line ab. ["the line ab" means the straight line that contains the points a and b] (ii) What is the slope of the line ab? (iii) The point c lies on the line ab. The r coordinate of the point c is -8. What is the y coordinate of the point c? (iv) Calculate the distance between the points a and b, correct to 2 decimal places.

Transcript

00:01 All right, so we have two points here, a and b, and the first thing we want to do is find the equation of these points.

00:07 And so i already have the equation of a line up here.

00:10 It's that y equals m x plus b and the equation for our slope m because we're going to need that to be able to figure this out.

00:16 So our points are always x comma y.

00:20 And then we label the first point as x1, y1 and the second as x2, y2.

00:26 And then we can find our slope just by replacing those numbers into this equation, that m equation.

00:32 So we are doing negative 2 minus 1 on the top and 2 minus negative 3 on the bottom, which simplifies to negative 3 over 5, that's our slope, and then we can go and plug that into this m right here in our y equals mx plus b.

00:48 So y equals negative 3 fifths x plus b.

00:53 In order to find our b, we do need to figure this guy out as a number.

00:58 We're going to plug in one of our points.

01:00 We're just going to use point a, where i'm going to replace the x with negative 3 and the y with 1 in this equation.

01:13 And so we are multiplying a fraction here, and when we multiply fractions, we do the tops together and the bottoms together.

01:20 Negative 3 doesn't really look like a fraction here, but secretly there's a 1 on the bottom, and so we can multiply the tops, negative 3 and negative 3 to get us 9, and on the bottom 5 times 1 to get us 5.

01:31 Then we just need to solve for b, so we're going to subtract this 9 fifths.

01:36 We're doing 1 minus 9 fifths here.

01:39 1 is really 5 fifths, and so then we can subtract this.

01:44 So since we have that common denominator, we leave the common denominator the same and do the subtraction on the top, 5 minus 9, to get negative 4, and that's our b value.

01:53 Now we have b all by itself.

01:55 So again we can go back up and we can plug this into our equation.

01:59 We leave the x and the y as letters but we do want to have this be be this specific number.

02:06 And so there's our answer for number one.

02:09 Luckily for us number two actually goes along with what we already did because it told us to find the slope of this line and we had to do that to write write this equation, the slope is that negative three -fifths we found.

02:24 So there's our answer for number two.

02:26 Wonderful...

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