6.3 NOTES – Standard Form (finding x- and y- Intercepts) and using intercepts for Quick Graphs
Name _____________________________________________
The standard form of a linear equation is:
Date ________________
Ax + By = C (A, B and C are real numbers)
How To find the x- and y- intercept from an equation written in Standard Form:
EXAMPLE:
Find the x- and y-intercept for this equation:
3x + 4y = 12
STEP 1 (find the x-int)
STEP 2 (find the y-int)
3x + 4y = 12
3x + 4y = 12
3x + 4(0) =12 (substitute 0 for “y” and solve for x)
3(0) + 4y =12 (substitute 0 for “x” and solve for y)
3x + 0 = 12
0 + 4y = 12
3x = 12
4y = 12
x=4
y=3
The “x-int” is: (4, 0)
The “y-int” is: (0, 3)
NOW, you can use those intercepts to plot the equation on a graph and draw your line:
(0, 3)
(4,0
)
To find the slope of the line you can either:
1.
or
=
Look at the graph and count :
OR
2.
=
Use the slope formula using the two intercepts you found [(0, 3) ( 4, 0)]:
=
Now you can answer this question:
find the slope, slant and intercepts for this equation: 3x + 4y = 12
m=
slant =
down (negative)
x-int. = ( 4, 0)
y-int. = ( 0, 3)
MORE EXAMPLES (with answers):
1.
-4x + 2y = 4
=
m:
slant:
up (positive)
2. -3x – 4y = 24
or 2
9x – 3y = 18
=
m:
=
m:
=
slant : down (neg)
slant: up (pos)
x-int:
(-1, 0)
x-in.:
(-8, 0)
x-int: (2, 0)
y-int:
( 0, 2)
y-int:
(0, -6)
y-int: (0, -6)
=
or 3