Graphs of Linier Equations
Graphs of Linier Equations
Graphs of Linier Equations
These are two forms are the most commonly used ways to
write linear equations.
1. Slope Intercept Form: y= mx + C
2. Standard Form: Ax + By = C
m = gradient/slope
C = constant
A and B = Coefficient
Parts of a Coordinate Plane
Y-Axis
To sketch the graph of an equation,
x y = 2x + 3 (x, y)
2 y = 2(2) + 3 = 7 (2, 7)
1 y = 2(1) + 3 = 5 (1, 5)
0 y = 2(0) + 3 = 3 (0, 3)
1 y = 2(1) + 3 = 1 (1, 1)
Copyright
by Houghton
Mifflin
y = 2(2) + 3 = 1 (2, 1)
7
2 Company,
Inc. All rights
reserved.
2. Plot the points in the coordinate plane.
x y (x, y)
2 7 (2, 7) y
8
1 5 (1, 5)
4
0 3 (0, 3)
x
4 4 8
1 1 (1, 1)
4
2 1 (2, 1) Copyright
by Houghton
Mifflin
8 Company,
Inc. All rights
reserved.
3. Connect the points with a straight line.
x
4 4 8
4
Copyright
by Houghton
Mifflin
9 Company,
Inc. All rights
reserved.
Exercise :
1. Plot the graph of these equetion on the
same cartesian plane.
a. y = 2x
b. y = 3x 5
c. y = -2x + 4
2. X-Intercept AND Y-Intercept
2x + 3y = 6 2x + 3y = 6
2x + 3(0) = 6 2(0) + 3y = 6
2x = 6 3y = 6
x=3 y=2
The x-intercept is 3. The y-intercept is 2.
Note: Note:
X-intercept (y = 0) Y-intercept (x = 0)
Example:
2. Find the y-intercept and x-intercept from the graph
1) xy=5
2) 2x + 3y = 12
3) 4x = 12 + 3y
4) 2x + y = 7
5) 2y = 20 4x
2. Find the x-intercept and y-intercept of each graph
a. b.
3. SLOPE/GRADIENT
rise y (change in y)
slope slope
run x (change in x)
y2 y1
slope
x2 x1
What does the line look like when
Zero
NO
slope is
slope.
zero fun!
Oh No!!!!
Slope Mountain
Ski Resort
1.Finding Slope from a Graph
1) Determine the slope of the line.
slope
example,
x2 x1
1. Find the slope of a line that goes through (-3, 5) and (2, 18)
-3 5 2 18
X1 y1 X2 y2
y2 y1 13
slope
x2 x1 5
Exercise
1. Find the slope of the line that passes through
a. (3, 5) and (-1, 4)
b. (9, 2) and (8, -7)
c. (-4, 4) and (-7, 2)
d. (5, -1) and (9, -4)
e. (3,7) and (5, 19)
3.Finding Slope and y-intercept from an equetion
y = 3x +
slope = 3
y-intercept =
2nd way: Another method to
find the slope if given
an equation of a line
is to write the equation
in the form Ax + By = C.
A B C
8x + 11y = 7
2. -3x + 9y + 9 = 0 5. y = -3x + 1
2
3. y x 1 6. 4x = 3y - 12
3
4. Finding the Equation of a Line from the Slope
one Point on the Line
Ans:
1st : Find gradient/slope
2 1 5 3
m= = =2
2 1 21
Equation of the line is y = 2x + b
2nd: Subtituting one points (either one will do) into the
equation
3 = 2.1 + b
32=b
b=1
So, we have the full equation of this line is y = 2x + 1
Exercise
1.Work out the equation for each straight the line,
given the gradient/slope and one point on the line
No Gradient/Slope Point
1. 2 (3,2)
2. -5 (-1,3)
3.
1 (2,1)
4
2. Write down the equation of the line that is parallel to the
given line and passes through the given point
No Point Equation
1. (4,3) X + 2y = 3
2. (5,2) x 2y + 3 = 0
3. (-4,-1) 4y + x = -8
3. Find the equation of the line that passes through
each of these pairs of points.
a) (0,5) dan (2,0)
1 3 1
b) ( , 1) ,
2 4 2
c) (-3,-5) and (-1,3)