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# Maths A-Level Help watch

1. I have 2 questions i'd like help with:
1: The line y =(1/4x)+2 meets the y axis at the point B. The point C has the coordinates (-5,3) find the gradient of the line joining point B to C.

2:The lines y=x and y=2x-5 intersect at the point A. Find the equation of the line with gradient 2/5 that passes through the point A. Hint solve y=x and y=2x-5 simultaneously.

Once again any help is appreciated if someone could show me workings and possibly why they did each step that would be perfect
2. (Original post by TehBrewer)
I have 2 questions i'd like help with:
1: The line y =(1/4x)+2 meets the y axis at the point B. The point C has the coordinates (-5,3) find the gradient of the line joining point B to C.

Once again any help is appreciated if someone could show me workings and possibly why they did each step that would be perfect
Let's go through the first question, I'm sure you'll find this easy...

What's the coordinates of B? Think about it, if it meets the y-axis, automatically you know the x-coordinate. You also know the y-coordinate then...
You know the coordinates of C.

Remember the formula to calculate gradient? m=(y2-y1)/(x2-x1)
You should get this..
3. For the first question the line crosses the y axis at point B - the y intercept. The y intercept can be found by setting x=0 into the equation of the line. So you will get (0,B). The gradient of BC is Δy/Δx so you will find the difference between the y coordinates of B and C and also the x coordinates of B and C
2. To find the point of intersection you set the 2 equations equal to each other as y=x and y= 2x-5 so this must mean that x=2x-5 which is simple enough to solve. Then use the equation of a line y-y1=m(x-x1) where the x1 and y1 are a pair of coordinates that the line passes through - point A. m is the gradient of the line = 2/5. You can then rearrange the equation of the line into the form of y=mx+c although you don't really need.
4. B is on the y-axis, thus has a x-coord of 0. To find it's y-coord, input x=0 into the equation of the line which it's part of: y = 1/4*0 + 2 = 2. Thus, B = (0,2).
The gradient of the line joining (x1,y1) and (x2,y2) is y2-y1/x2-x1(=y1-y2/x1-x2). Thus the gradient of the line joining point B to C is 3-2/-5-0 = -1/5

2)First, solve the two equations by equating them (which we can do as they are both equal to y) y = x = 2x-5 --> x = 2x+5 --> 0=x+5 ---> x = -5; and as y=x, y = -5.
The equation of a line with gradient m, on which lies point (x1, y1), is y-y1=m(x-x1). Thus y - (-5) = m(x -(-5)), thus y+5 = m(x+5). We have been told that m=2/5, thus y+5 = 2/5(x+5), thus y = 2/5(x+5) -5

Keep going! I bid you well!

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