The general equation for a straight line is given by y = mx + c.
"m" is the gradient and
"c" is the value of the intercept the line makes with the vertical axis.
Let's start with an example y = (5/4) x + 2 .
The intercept that the straight line will make with the vertical axis is "+2" indicated by the red dot in Diagram 1.
Diagram 1
Next, we noticed that the gradient is m = (5/4). This meant that the vertical change is 5 units upwards (positive number) for a horizontal change of 4 units in the positive (right-going) direction. Let's find the other spot on the straight line. (Diagram 2)
Diagram 2
The other spot is identified after moving from the first red dot 5 units up and 4 units right. The unit movement is based on the gradient (m = 5/4) set in the equation.
Note: To draw a straight line graph, we only need 2 points.
With the 2 points identified, we are now ready to draw the line connecting the 2 red points.
Diagram 3
To summarise, we just need to follow 3 steps:
- Identify the intercept (c) from the equation and indicate it on the vertical axis
- Find the other point using the gradient (m) as a guide with the point in step 1 as start reference
- Connect the 2 points identified to obtain the straight line graph
This is as simple as A B C !
Another example: y = -2 x + 7.
The y-intercept is "+7" and the gradient is "-2", meaning, a drop of 2 units for 1 unit movement to the right. The graph is shown below (Diagram 4).
Diagram 4
Let's celebrate!
:)
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9 comments:
thanks!!!
still confused pls help
Just focus on 2 items; the gradient and y-intercept. The gradient is the ratio of the number of units in the vertical to horizontal drawn. A good starting point to drawn the 2 points needed to form a straight line is the y-intercept. This is a point directly on the y-axis (with x=0). After which, move the units from this starting point by the amount stated in the value of the gradient. This will let you get the second point needed. With the 2 points, simply connect them up with a straight line. :-)
What's the gradient mean?! In simple terms.....
In short, a gradient is a number that tells one how steep is the slope.
Example: A number of 10 is steeper than a number of 3.
You can imagine a car going up a slope.
With a slope of 10, the car needs more "power" to go up the slope while a slope with a 3 will requires a much lesser "power" that the fomer slope with 10.
why do we drop 2 units for 1 unit movement to the right? im lost?
In reply to peter_rulz_10,
there are 2 movements in plotting a marker (or point in a graph).
They are the vertical and horizontal movement or direction. They are represented as the y-axis and x-axis respectively.
2 units drop meant a movement downwards along the y-axis and at the same time another movement going to the right along the x-axis of 1 unit.
==> These motions enable one to create the new marker (or point) for the straight line drawing.
what would you do if you are given the data in form of a word puzzle. So say they just tell you a car has travelled a certain distance in a certain amount of time plot this as a graph showing the gradient...
How would you work out the gradient in the first place and how could you plot this
My suggestion is to plot the time taken on the x-axis(horizontal axis) with the distance travelled on the y-axis (vertical axis). With the given data of time and distance, you should be able to get one marker on the graph. The other marker needed to create the straight line will be the origin (0,0). Joining these 2 markers will be the straight line. Gradient can be gotten by m = (distance / time taken).
However, if the objective of the question is to find the speed of the car, you can simply use speed = distance travelled / time taken without plotting the graph.
There are many tools in maths, selecting the appropriate ones is the real target behind learning maths.
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