weekly maths homework

Please remember to show all work on every problem.

Name________________________________

1)  Find and write the x and y intercepts and one other ordered pair in the space below that satisfies the following equation.   Graph the line through these three points.  You may use the grid provided or create your own graph.  Show all work. (10 pts)

3y=-4x+9

Y=-4/3x+3

Y –intercept is 3

4x=-3y+9

X=-3/4+2.25

x-intercept=2.25

the ordered pair is

(2.25,3)

The other two ponts are (2.25,0)  and (0,3)

2) Write an equation of a line through the point (-3, 2) that is parallel to the x-axis.  Graph the line on the grid below or create your own graph.  State the slope of this line. (5 pts)

Parallel lines have equal slopes x –axis has the equation y=0

Therefore the equation is y =2

The slope is 0

3) Given the linear equation: , find the slope and y-intercept of the line.  Show all work below. (5 pts)

Y=mx+c

Y=4x-8

Slope is 4

While the y-intercept is -8

4) Given the points (-5, 27) and (2, -1):

a)  Find the slope of the line through the points. (1 pt)

slope=change in y /change in x

therefore 27- -1/-5-2

28/-7

Slope = -4

b)  Write an equation in point-slope form of the line through the points. (2 pts)

y =mx+c

y+1/x-2=-4

y+1=-4(x-2)

y=-4x-3

c)  Convert the equation to slope-intercept form. (2 pts)

y=-4x-3

d)  Graph the equation.  Give the coordinates of at least two points on the line.  You may use the axes provided, or create your own graph. (2 pts)

5) Answer the following questions:

a) Write an equation of a vertical line through the point (7,-3).  (2 pts)

The line being vertical it means that its parallel to the y- axis which is also the x=0

Therefore the equation is x=7

b) Write an equation of a horizontal line through the point (0,5).  (2 pts)

if its horizontal it means its parallel to the x-axis which is also the line y=o

therefore the equation will be y=5

            c) Find the slope of a line perpendicular to the line with equation 2x + 3y = 18. (2 pts)

2x+3y=18

3y=-2x+18

Y=-2/3x+6

Slope is

-2

3x

6)  The median sale price of new homes sold in the United States in 2007 was $248,000.  In 2010, the median price decreased to $222,000.  Let y be the median new home sale price in the year x, where x = 0 represents the year 2007. 

a) Write a linear equation that models the change in the median new home price in terms of x.  [Hint: the line must pass through the points (0, 248,000) and (3, 222,000)].  (3 pts)

slope= change in y/ change in x

248000-222000/0-3

=26000/3

y-222000/x-3=26000/3

3(y-222000)=26000(x-3)

3y-666000=26000x-78000

3y=26000x-78000+666000

3y=26000x+744000

Y=26000/3x+744000/3

b) Explain what the slope for this line means in the context of the problem. (2pt)

The slope is the difference of median price between 2007 and 2010 divided by the time interval.

c)Use this equation to predict the median new home price in the year 2014.  (2 pt)

7) Given:

a)      Solve for x.  (3 pts)

15+2x>4x-7

15+7=4x-2x

22=2x

Therefore x=11

b)      Express your answer in Interval Notation.  (1 pt)

c)      Graph your answer to part a.  (1 pt)

8)  Given

a)      Solve for x.  (3 pts)

-4<-2x+4  <

-12<-2x+4<18

-2x=18-4+12

-2x=26

-x=13

X=-13

b)      Express your answer in Interval Notation.  (1 pt)

c)      Graph your answer to part a.  (1 pt)

Bonus:  Write an equation in point-slope for of the line through the point (-1,2) parallel to the line with equation 4x - 3y = 1.  Show all work.  (5 pts.) 

Parallel lines have equal slope (gradient)

Therefore

Y=mx+c

3y=-4x+1

Y=-4/3x+1/3

Slope being-4/3

The equation of the point  (-1 ,2) is

y-2   =-4/3

x+1

3y-6=-4x-4

3y=-4x-4+6

3y-4y+2