Drawing the Line
- Author:
- Jaime Dianzon, Tim Brzezinski
- Topic:
- Algebra, Coordinates, Linear Equations
Where do you draw the line?
OBJECTIVE: To graph a line on the Cartesian plane using points
There's a postulate in Geometry that 'two points determine a line.'
So if you're given two points, just plot them, draw a straight line passing through both points, and your job is done!
In previous exploratory activities, you've probably discovered how to do this.
Taking the First Bite (https://www.geogebra.org/m/ufyfkdr4)
Putting Things in Perspective (https://www.geogebra.org/m/kxzydnyz)
Getting Off the Grid (https://www.geogebra.org/m/hqa3etew)
Sharpening Your Tools (https://www.geogebra.org/m/vjvjqs2z)
Standing at Sword's Point (https://www.geogebra.org/m/un8uh2zr)
You can also graph a line by constructing a table of values (at least two ordered pairs), plotting the points, and passing a line through them.
Toeing the Line (https://www.geogebra.org/m/pfkb67ek)
NOW ... instead of plotting randomly generated pairs of coordinates, you can use two special points—the x-intercept and the y-intercept.
If the intercepts are not already given, you can easily derive them from the STANDARD FORM of a line (Ax + By = C) by using these formulas: x-intercept = C/A and y-intercept = C/B.
Traveling on the Standard Line (https://www.geogebra.org/m/chu2bn3u)
On the top left-hand corner of the applet below, you'll see a linear equation in STANDARD FORM.
Use the following formulas to fill in the boxes:
slope (m) = -A/B
x-intercept = C/A
y-intercept = C/B
If you type in the correct values and your graph is correct, you'll see a big "CORRECT !!!" sign appear.
Repeat as many times as needed to master the concept.
The applet below is similar to the one above, except that the boxes for the slope and the intercepts have been left out.
Move the WHITE DOTS to graph the x- and y-intercepts.
If your graph is correct, you'll see a big "CORRECT !!!" sign appear.
Repeat as many times as needed to master the concept.
TODAY you learned how to graph a line on the Cartesian plane using the intercepts.
In future lessons, you'll learn how to graph a line on the Cartesian plane using other sets of information. We hope you ENJOYED your GeoGebra adventure!