ch.3 continued

ch.3 pg. 178 ex.7

graph the equation 2x-3y=6
by using the x and y intercepts.
solution:

to find the x intercept let y=0 in the equation 2x-3y=6
2x-3.0=6
2x=6
x=3
the x intercept is (3,0),
to find the y intercept, let x=0 in 2x-3y=6

2.0-3y=6
-3y=6
y=-2

hint:

the cover up method could be used;
ex. 2x-3y=6
cover up 3y to figure out the x intercept.
2x=6
x=3
the x intercept is (3,0)

the 2x could be covered up to find the y intercept.
-3y=6
y=-2
the y intercept is (0,-2)

3.2 slope: pg. 187

the slope formula is m=slope=rise/run=change in y coordinate/change in x coordinate.

ex. 1. finding the slope of a line.
a slope uses the coordinates on the graph of the line from pt. a to pt. b.

solution:

the coordinate of pt.a is (0,4) and the coordinates of pt.b are (3,0).
going from pt. a to pt. b, the change in y is -4 from the +4,
and the change in x is a positive 3.

m=-4/3=-4/3 it is y/x y over x.
the y coordinates rises or increases by 4 units, and the x coordinates decreases by 3 units or run is -3. the rise over run is +4/-3 or - 4/3 go up on the graph beginning at 0 on the y axis and go or rise up 4 and go down from the 4 to a -3
number.

m=2/3

on the graph starting at 0 on the y axis and go up 2 then over 3, and continue this on every pt. as the points continue, it is rise or up over run decrease or to go over.

3.3 equations of lines in slope intercept form:

ex. 1. slope intercept form.

y2-y1/x2-x1 = m slope formula

consider the line through (0,1) with slope 2/3.
we can use the points (x,y) and (0,1) in the slope formula.

y-1/x-0=2/3 let x1,y1= (0,1) and (x2,y2)=(x,y)

in slope format is y-1/x-0=2/3
y-1/x=2/3
now solve the equation for y
mutiply each side by x.
x.y-1/x=2/3.x
y-1=2/3x
y=2/3x+1 add 1 to each side.

the formula to find the intercept pts. using the slope infromation; the formual is y=mx+b.

that is all for now.

Marie Zajac
Bachelor of Arts degree in psychology with a concentration in rehabilitation in counseling. CPC a certified life coach