# Thread: Finding point of intersection

1. ## Finding point of intersection

I have been asked to draw a graph of the line that passes through the point (-4, -2) and has a gradient of 2!

Have done that

Next question is Find the point of intersection of the above line with the line y = -x + 2

How do i go about doing that? can someone please explain? Do i need to do a table of values?

2. Originally Posted by BsMummy
I have been asked to draw a graph of the line that passes through the point (-4, -2) and has a gradient of 2!

Have done that

Next question is Find the point of intersection of the above line with the line y = -x + 2

How do i go about doing that? can someone please explain? Do i need to do a table of values?
To make a table of values, you have to know the equation. You are only given a point, and a gradient. This means you must derive the equation. If the gradient is 2, then we can use the equation $y=mx+b$ to write:

$y=2x+b$

You know that the point (-4,-2) is on the line. This means that:

$-2=2(-4)+b$

Sovling for b:

$b=6$

The equation of the line can now be written.

$y=2x+6$

To find the point where the lines intersect, you have to solve the system of equations:

y=2x+6
y=-x+2

The solutions for x and y will give the point of intersection.

3. Oh, I forgot that you need to graph the line to. To draw the graph, find the y-intercept by seting x=0.

y=2x+6
y=6 is the y intercept, which is the point (0,6).

You were already given another point on the line in the statement of the problem. Plot that point, and the y-intercept, and then draw the line through those points.

4. im dumb and all that has gone way over my head! also i thought it was
y = mx+c - or is that the same as y = mx+b?

5. Originally Posted by BsMummy
im dumb and all that has gone way over my head! also i thought it was
y = mx+c - or is that the same as y = mx+b?
That is exactly the same, just a different name for the variable.

6. Originally Posted by BsMummy
im dumb and all that has gone way over my head! also i thought it was
y = mx+c - or is that the same as y = mx+b?
Ok, it sounds like you need an much more involved tutorial on this subject.

This video will help you understand how to find the equation of a line when you are given the slope and a point. Write down what I showed you above, and compare that to what they do in the video.

YouTube - Watch Video on Writing the Equation of a Line - Algebra Help