Download Slope -intercept form - EWA Seventh Grade Eagles

SLOPE INTERCEPT
FORM
Objective: In this lesson you will
learn to derive the equation and
y=mx+ b by using similar triangles.
SLOPE-INTERCEPT
FORM
Slope can be use to find the equation
of a given line. When that line crosses
the y-axis not at the origin (0,0). The
general equation is
y  mx  b
where the m is the slope of the line
and b is the y-intercept.
This is Slope-Intercept Form.
SLOPE-INTERCEPT
y  mx  b
Slope
y-intercept
Y-INTERCEPT
 What
is the y-intercept?
The y-intercept is the point where the line
crosses the y-axis. The vertical distance
from the origin.
This point is (0,y), x is always zero at this
point.
y-axis
y-axis
y-intercept
x-axis
x-axis
y-intercept
HOW DO WE FIND y  mx  b?
Create a triangle with slope
2
3
Now we can make a triangle
out of any coordinate (x,y),
with slope y  2 x since we are
no longer at the origin.
y2
y2 2
So

x
3
Cross
Multiply
3
2
 0 ,2 
x
3
2
y2
x
 0 ,0 
3 y  2   2 x  3 y  6  2 x
2
Solve for y  3 y  2 x  6  y  x  2
3
HOW DO WE FIND y  mx?
Create a triangle with slope
m
Now we can make a triangle
out of any coordinate (x,y),
with slope y  b
x
1
y b
x
x
1
m
x
1
m
 0,b 
 0 ,0 
y b
So y  b  m
1
Cross
Multiply
y  b  mx
 y  mx  b
Thus we have the
slope intercept form.
REMEMBER:
Any point (x,y) on a line across the yaxis with slope m will satisfy
y  mx  b
y  mx  b is the equation of a line
that crosses the y-axis with
slope=m.
TRY THIS!!
Create a triangle with slope
-3
1
Now we can make a triangle
out of any coordinate (x,y),
with slope y  2
x
3
 0 ,2 
x
x
1
3
y2
So y  2   3
x
1
Cross
Multiply
y2
1
 0 ,0 
y  2  -3 x  y  -3x  2
TRY THIS!!!!
Use similar triangles to demonstrate that
the equation of a line that passes through
the point (0,-2) with slope 4 is y  4 x  2
Create a triangle with slope
4
1
1
1
y   -2 
4
4
x
So y   -2   4 Cross
Multiply
x
1
y  2  4x  y  4x  2
 0 ,0 
 0,-2 
y   -2 
x