Exercise: Equations Of Lines And Graph Plotting.

1 GEOMETRY:

equations of lines and graph plotting.

a Find below an empty y-valued table for random x values:

x -4 -2 0 2 4

y - - - - -

i Fill the table with the corresponding y values for each x value, by using the equation y = 2x − 2.

ii Plot each x and y value as points (coordinates) on a grid, and mark these points with a visible cross. For each point drawn on the grid, write down its coordinates (x,y). What do you notice? Now draw a line passing through all the points you have drawn using a ruler.

1 b Find below an empty y-valued table for random x values:

x -5 -2 0 3 5

y - - - - -

i Fill the table with the corresponding y values for each x value, by using the equation y = 2x.

ii Plot each x and y value as points (coordinates) on a grid, and mark these points with a visible cross. For each point drawn on the grid, write down its coordinates (x,y). What do you notice? Now draw a line passing through all the points you have drawn using a ruler.

iii Compare the lines drawn in exercises a)ii and b)ii. How are they similar, and how are they different? Compare them graphically (in terms of the lines you have drawn) and algebraically (their equations). The equation of the first line is y = 2x − 2, while the second line’s equation is y = 2x. What do you think is the purpose of the -2 term in the first line equation? 2

c Find below an empty y-valued table for random x values:

x -3 -2 0 1 2

y - - - - -

i Fill the table with the corresponding y values for each x value, by using the equation y = 3x.

ii Plot each x and y value as points (coordinates) on a grid, and mark these points with a visible cross. For each point drawn on the grid, write down its coordinates (x,y). What do you notice? Now draw a line passing through all the points you have drawn using a ruler.

3 d Find below an empty y-valued table for random x values:

x -3 -2 0 1 2

y - - - - -

i Fill the table with the corresponding y values for each x value, by using the equation y = −3x.

ii Plot each x and y value as points (coordinates) on a grid, and mark these points with a visible cross. For each point drawn on the grid, write down its coordinates (x,y). What do you notice? Now draw a line passing through all the points you have drawn using a ruler.

iii Compare the lines drawn in exercises c)ii and d)ii. How are they similar, and how are they different? Compare them graphically (in terms of the lines you have drawn) and algebraically (their equations). The equation of the first line is y = 3x, while the second line’s equation is y = −3x. What do you think is the purpose of the negative sign in the second line equation?

4 2 OPTIONAL/CHALLENGE: In depth analysis of line equations in Cartesian form.

e The equation of a line in Cartesian two-dimensional coordinates is: y = mx + c. We know x is the input variable, while y is the output variable. y depends on x, so we call x the independent variable (input) and y the dependent variable (output).

i Research the term Cartesian. What does it mean? What do we mean by a 2D grid? (otherwise known as a 2D Cartesian coordinate system.)

ii Research the terms independent and dependent variables. What do they mean?

iii Inspect the general form y = mx + c of a line. The terms m and c are constants in the equation, meaning they do not change, no matter what the input value of x is. Research the purpose of the constants m and c. You should be able to figure it out from the previous questions. If not, research online.

iv y is a function of x. What does that mean?

v You should now have a good understanding on all of the terms used in the descri ption (part e). Read the descri ption once more, ensuring it makes sense. Practice your understanding by defining and writing down the more complicated terms used in the descri ption with no help or guidance.