Use the table function on the calculator to obtain co-ordinates to plot for the following equation:

y = ⅓x + 3

Starter: Plot the following graphs

y = 5x – 3 y = 2

y = -2x + 1 x = -3

y = ¼x + 3 y = -x + 1

To find the equation of a line, use the general form of a linear equation:

y = mx + c

Note 2: Finding Linear Equations from Graphs

gradient y-intercept

−6 −4 −2 2 4 6

−4

−3

−2

−1

1

2

3

4

x

y

Example – find the equation of this line

Locate two points on cross-gridlines

These are the corners of a triangle

Find the lengths of the two sides (rise is 3 and run is 2)

3

2

Write the fraction RISE/RUN.

23

If the line leans LEFT, then negative 23

m

−6 −4 −2 2 4 6

−4

−3

−2

−1

1

2

3

4

x

y

Find the y-intercept, C = 1 Use your values of m and c to write the equation

y = mx + c becomes

123

xy

Graphics Calculator instructionsUse the stats function to find equations.

Stats Function Delete any data in columns: (F6) DELA (F4), YES (F1)Enter co-ordinates: (X – List 1, Y – List 2) SET (F6): Graph type Scatter

X List List 1Y List List 2

EXITGraph points: GPH1Draw line: CALC (F1), X (F2) - Linear line, aX + b (F1)

Now try to find the equations of these graphs

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

m = 2/2 = 1

c = – 2

y = 1x – 2 or

y = x – 2 (ans)

m is positive as it leans to the right

m = - 4/2 = –2

c = 3

y = – 2x + 3 (ans)

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

m is negative as it leans to the left

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

m = 2/6 = 1/3

c = -3

y = 1/3 x – 3 (ans)

m is positive as it leans to the right

m = - 2/3

c = 1

y = – 2/3 x + 1 (ans)

m is negative as it leans to the left

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

Note that we could have also drawn our triangle here

or here

Remember that, regardless of how you’ve drawn your triangle, the ratio RISE : RUN in this question will always be 4:6 or 2:3 i.e.

m = 2/3

m = 3/4

c = 0

y = ¾ x

m is positive as it leans to the right

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

NOTE If it goes through the origin then the y intercept = 0, so there will be no “c” on the end of the equation!

No c

m = - 5/5 = –1

c = 0

y = – x

m is negative as it leans to the left

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

AGAIN it goes through the origin, so y intercept is zero and there won’t be a “c”

Drawing the graph using the gradient and y-intercept

Example – Plot the line y = 2x – 3 using gradient and y-intercept

STEP 1 Plot the y-intercept, – 3

x

y

-5

-4

-3

-2

-1

1

2

3

4

5

STEP 2 Write the gradient as a fraction

12

m

The rise is 2

The run is 1

And it leans to the RIGHT (+)

STEP 3 Beginning at the y-intercept,– 3, make a triangle whose horizontal is 1 and vertical is 2. Plot a point.

STEP 4 Now we have 2 points! Join this new point to the y-intercept. Arrows on ends and label line

Y =

2x -

3