starter: plot the following graphs y = 5x – 3 y = 2 y = -2x + 1 x = -3
Post on 22-Feb-2016
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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
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