where the two lines cross is called their point of intersection
Here we will cover a method for finding the point of intersection for two linear functions. That is, we will find the (x, y) coordinate pair for the point were two lines cross.
Our example will use these two functions:
f(x) = 2x + 3
g(x) = -0.5x + 7
We will call the first one Line 1, and the second Line 2. Since we will be graphing these functions on the x, y coordinate axes, we can express the lines this way:
y = 2x + 3
y = -0.5x + 7
Those two lines look this way:
Now, where the two lines cross is called their point of intersection. Certainly this point has (x, y) coordinates. It is the same point for Line 1 and for Line 2. So, at the point of intersection the (x, y) coordinates for Line 1 equal the (x, y) coordinates for Line 2.
Since at the point of intersection the two y-coordinates are equal, (we'll get to the x-coordinates in a moment), let's set the y-coordinate from Line 1 equal to the y-coordinate from Line 2.
The y-coordinate for Line 1 is calculated this way:
y = 2x + 3
The y-coordinate for Line 2 is calculated this way:
y = -0.5x + 7
Setting the two y-coordinates equal looks like this:
2x + 3 = -0.5x + 7
Now, we do some algebra to find the x-coordinate at the point of intersection: 2x + 3 = -0.5x + 7We start here.2.5x + 3 = 7Add 0.5x to each side.2.5x = 4Subtract 3 from each side.x = 4/2.5Divide each side by 2.5.x = 1.6Divide 4 by 2.5.
So, we have the x-coordinate for the point of intersection. It's x = 1.6. Now, let's find the y-coordinate. The y-coordinate can be found by placing the x-coordinate, 1.6, into either of the equations for the lines and solving for y. We will first use the equation for Line 1:
y = 2x + 3
y =2(1.6) + 3
y = 3.2 + 3
y = 6.2
Therefore, the y-coordinate is 6.2. To make sure our calculations are correct, and also to demonstrate a point, we should get the same y-coordinate if we use the equation for Line 2. Let's try that:
y = -0.5x + 7
y = -0.5(1.6) + 7
y = -0.8 + 7
y = 6.2
Well, looks like everything has worked out. The point of intersection for these two lines is (1.6, 6.2). If you look back at the graph, this certainly makes sense:
Here's the summary of our methods:
Actually, there is nothing special about the functions being linear functions. This method could be used to find the point or points of intersection between many other types of functions. One would express the functions in 'y =' form, set the right side of these forms equal to each other, solve for x, (or x's), and use this x, (or x's), to find the corresponding y, (or y's).
Here's a calculator to help you check your work. Make up two linear functions in slope-intercept form. Calculate the point of intersection using the above methods. Then enter the slope and y-intercept for each line into the calculator and click the button to check your work.
Vertex
No, two straight lines can intersect at only one point and that is their point of intersection.
When two lines intersect they form an axes.
Two lines cross or intersect at a point.
If they do intersect, it will be at their point of intersection.
The intercept
Vertex
Two lines intersect at a point
The point of intersection.
If two different lines intersect, they will always intersect at one point.
yes two lines intersect to form a point two planes intersect to form a line
No, two straight lines can intersect at only one point and that is their point of intersection.
When two lines intersect they form an axes.
Two lines cross or intersect at a point.
Two lines cross or intersect at a point.
The lines that intersect to Form A right triangle are called Perpendicular Lines; the resulting meeting point of these two lines is called the vertex of the angle.
If they do intersect, it will be at their point of intersection.