ch3. slope intercept form .

pg. 205

slope intercept form;
y=mx+b start at the y intercept (0,b); and count off the rise and run.

standard form; Ax+By=C

find the x intercept by setting y = 0. Find the y intercept by setting x = 0. Find one additional point as check.

a). the line through (0,3) that is paralell to the line y=2x-1.
solution;
the line y=2x-1 has slope 2 and any line paralell to it has a slope 2.
The equation of the line with y intercept of (0,3) and slope 2 is y=2x+3

b). the line through (0,4) that is perpendicular to the line 2x-4y=1
solution:
First find the slope of 2x-4y=1
-4y=-2x+1
y=1/2x-1/4

point slope form:

slope formula; y2-y1/x2-x1=m

let m=2/3 (x1,y1)= (4,1) and (x2,y2)=(x,y)
y-1/x-4=2/3
y-1=2/3.(x-4) multiply each side by x-4.
the slope is 2/3

point slope form

y-y1=m(x-x1)


That is all for now.

Marie Zajac
BA in Psychology with a concentration in Rehabilitation in Counseling.

algebra a system with no solution pg.453 and more

pg. 453 ex. 453

ex. 3

2x-3y=6
3y-2x=3

solution:

first write the equation in y slope intercept form;

2x-3y=6
-3y=-2x+6
y=2/3x-2
the +6 is taken off and the 2 is divided by 3x then bring the -2 with the equation.

3y-2x=3
3y=2x+3
the 3y is kept, the -2x on the left side becomes 0, bring the 2x on to the right side of the= sign then the - becomes a +.
y=2/3x+1

since the slope is the same 2/3, the lines then are paralell, with a 0 with a line through it to indicate the solution set as empty.

17. pg, 459

2y-2x=2
2y-2x=6

first rewrite the equation in slope intercept form;
y=x+1 and y=x+3
the lines are paralell with no solution and an empty set.

ex. 3 ch. 3 pg. 215

using point slope form with parallel lines:

find the equation of each line. Write the answer in slope intercept form.
a) the line through (2,-1) that is parallel to y=-3x+9

solution: the slope of y=-3x+9 and any line parallel to it is -3.
now use the point (2,-1) and slope -3 in point slope form.

y-y1=m(x-x1) point slope form.
y-(-1)=-3(X-2) substitution
y+1=3x+6 simplify
y=-3x+5 slope intercept form
since -1 = -3(2)+5 is correct, the line y=-3x+5 goes through (2,-1). It is parellel to y=-3x+9. So y=-3x+5 is the desired equation.

that is all for now.
Marie Zajac BA in Psychology with a Concentration in Rehabilitaion in Counseling.

7.1 pg. 459

#17. 2y-2x=2
2y-2x=6

rewrite in y slope intercept form.
y=x+1
y=2/2x is +1

ex. 4 graphing a line using y-intercept form and slope
graph the line 2x-3y=3
subtract 2x from each side.
-3y=-2x+3
2x-2x=0-3y=3-2x
-3y=2x+3 then divide both sides by -3
y=2/3x-1
the subtraction of 2-3=1 bring the x.
the slope is 2/3 and the y- intercept is (0,-1)

ex. 5 pg. 204
graphing lines with y intercept and slope.
a) y=-3x+4
solution:
first write the equation in slope intercept form:
the slope is -3 and the y intercept is (0,4), Because, -3=-3/1

b) 2y-5x=0
first solve the equation for y.
2y=5x
y=5/2x
the slope is 5/2 and the y intercept is 0,0.

the method of graphing depends on the form
slope intercept form y=mx+b Standard form is Ax+By=c

y=mx+b start at the y intercept of 0,b and count off the rise and run.
Ax+By=c find the x intercept by setting y=o and find the y intercept by x=0, and one additional point as check.

that is all for now
Marie Zajac BA in Psychology with a concentration in Rehabilitation in Counseling.

ch.7 ex. 7.1 exercise 13 algebra

question #13. pg. 459

13. y=2x+4
3x+y=-1

y=2x+4 is already in the y slope inter cept form
is a line with a slope of 2 and a y intercept of (0,4)

3x+y=1 is not in the y slope form.

or y=-1 or y=-3x-1 is a line with a slope of -3 and y intercept of (0,-1)
put y= on one side the left side of the equation, subtract 3 from both sides; placing the 3 from one side of the equal sign to the right side the 3 brcomes-3. The slope becomes -3, the intercept begins at 0,and 1 becomes(0,-1).

The lines on the graph intersect at (-1,2), the solution set then is (-1,2).

ex. pg. 216

3x+2y=8
2y=-3x+8
y=-3/2x+4 slope intercept form.

15. pg. 459

y=-1/2x+4 x+2y=8
this is in y intercept slope form.
this is the same as the first equation. All points on the line satisfies both equations. The solution set is (x,y) (x+2y=8)

that is all for now
Marie Zajac
Bachelor of Arts deggree in Psychology with a concentration in rehabilitation in Counseling.

7.1 exercises

pg. 459

#9 y=2x-1
2y=x-2

y=2x-1 is a straight line with y intercept of (0,-1), and a slope of 2.

in slope intercept form 2 is the slope.

the graph of 2y=x-2 or y=1/2x-1 is a straight line with y intercept of (0,-1) with the slope of 1/2.

ex. 2 pg. 453

2(y+2) =x
x-2y=4

has many solutions;

solution;
solve the system by graphing;

2(y+2)=x
2y+4=x
put into slope format
subtract 2 from each side and divide y1/x1/y2/y1
y=+2/4 1/2x
y=1/2x-2
2/4=1/2 x-2

x-2y=4
+x-2y=4
-2y=-x+4
then in slope intercept form;

y=2/4 1/2x-2
y=1/2-2

because the equations have the same slope intercept form, the original equations are equilevant. Their graphs are the same straight line. Every point on the line satisfies both equations of the system. Their are infinitely many points in the sokution set. The solution set is (x,y)

ch7 graphing

ch.7; 7.1,

exercises:

warm ups: true or false and explain:

1. the ordered pair (1,2) is in the solution set to the equation 2x+y=4

true because if x=1 and y=2 then 2(1)+2=4 is correct.

2. the ordered pair (1,2) satisfies 2x+y=4 and 3x-y=6

false, because if x=1 and y=2 then 3(1)-2=6 is incorrect. Both equations must be satisfied for the compound statement using and to be true.

3. the ordered pair (2,3) satisfies 4x-y=5, and 4x-y=-5


false because, (2,3) does not satisfy 4x-y=-5

4(2)-3=5 8-3=5 a true statement 4(2)-3=-5 not true the answer is 5 not a -5.

4. if two distinct straight lines in the coordinate plane are not parallel, then they intersect in one disticnt place.

true.

5. the substitution method is used to eliminate a variable.

true because when we substitute one of the variable are eliminated.

6. no ordered pair satisfies y=3x-5 and y=3x+1

true because each of these lines has a slope of 3 and are parallel.

7. the equation y=3x-6 and y=2x+4 are independant.

true because, the lines are not parallel and they have differant y intercepts.

8. the equation y=2x+7 and y= 2x+8 are inconsistant.

true because, the lines are parallel and have differant y intercepts.

9. the graphs of dependant equations are the same.

true because, dependant equations have the same solution sets.

10. the graphs of a linear equation intersects at exactly one point.

true because, a system of independent equations has one point in its solution set.

that is all for now.

Marie Zajac

Bachelor of Arts Degree in Psychology with a concentration in rehabilitation counseling.

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