Slope!
Graphing Linear Functions
Linear Fns Cont'd
Parallel and Perpendicular Lines
Scatterplots and Word Problems
100
Find the slope of the line from the graph below.
slope = -4/5
100
When given an equation in slope intercept form, where should you start when graphing the line?
the y-intercept (your b from y=mx+b)
b=begin!
100
What does the m represent from the equation y=mx+b? What does the b represent?
m=slope
b= y intercept
100
1) What is true about the slopes of parallel lines?
2) What is true about the slopes of perpendicular lines?
1) they are the same
2) they are negative/opposite reciprocals of eachother
100
During one month at a local deli, the amount of ham sold decreased as the amount of turkey sold increased. Is this an example of positive correlation, negative correlation, or no correlation?
negative correlation
200
What is the slope formula?
Answer: m= (y2-y1)/(x2-x1)
200
Identify the equation of the line graphed below. Write it in slope intercept form.
y= -4/5x -1
or
y-(-1) = -4/5(x-0) which is y=-4/5x-1
200
Rewrite the following equation from standard form into slope intercept form.
-2x + 7y= -14
7y = 2x - 14
y = 2/7x - 2
200
Are the following pairs negative reciprocals? Answer each!
1) -2 and 1/2
2) -3 and 3
3) 0 and -1/0
1) yes
2) no
3) yes
200
Ms. McGuinness is buying pictures from her recent Europe trip. An online print shop charges $0.25 per 4 x 6 inch print, along with a flat rate shipping charge of $6. If Ms. McGuinness has $25 to spend, how many prints can she order?
Ms.McGuinness can order 76 prints!
25 = 0.15x + 6
19= 0.15x
x = 76
300
Find the slope from the following two points:
(-4, -3) and (-7, 6)
slope = -3
300
Refer to the graph below. Write an equation in point slope form to represent the following line. Then, convert it to slope intercept form.
points: (0,4) and (5,2)
slope: (-2)/5 = -2/5
equation:
y-4= -2/5(x-0) -> y-4= -2/5x
-> y= -2/5x + 4
300
Write an equation in point slope form of the line that passes through the given points. Then, write the equation in slope intercept form.
(-2, 4) and (3, -1)
y = -x + 2
slope= (-1-4)/(3-(-2)) = -5/5= -1
y - 4 = -1(x+2) = y-4 = -x -2 gives: y=-x+2
300
Write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(1, -6) and x - 2y= 4
answer: y= -2x-4
300
Chelsea is selling candles and candy bags for a class fundraiser. Candles cost $12 and candy bags costs $4 each. If she sold 10 candles and made $168, how many candy bags did she sell?
12 candy bags
12x + 4y= 168
12(10) + 4y= 168 solve!
4y=48 -> y=12
400
What is the slope of a horizontal line?
A vertical line?
The slope of a horizontal line is 0.
The slope of a vertical line is undefined.
400
DAILY DOUBLE!
There are at least 2 ways to approach graphing the following equation.
Identify 2 approaches you could take and show your work for both (create the graph and show all work for each method)
equation: 6x - 2y =18
method 1) rewrite in slope intercept form!
-2y = -6x + 18
y= 3x -9 (GRAPH)
method 2) intercepts!
x-int: (3,0)
y-int: (0,-9)
400
Name the formulas for the following:
-standard form
-slope intercept form
-point slope form
standard form: ax+by=c
slope intercept form: y=mx+b
point slope form: y-y1=m(x-x1)
400
DAILY DOUBLE!
Answer whether each statement is always, sometimes, or never true.
1) Perpendicular lines have opposite/negative reciprocal slopes.
2) Two lines with the same slope and y intercepts are parallel.
3) Two lines with negative slopes are parallel.
1) Always true
2) never true -- this would refer to the same line itself!
3) sometimes- must be the same to be parallel with different y-intercepts
400
Refer to the following table.
1 Make a scatterplot of the data.
2) Describe the type of correlation the scatterplot shows.
3) Draw a line of best fit on the graph. Approximate the equation of the line in slope intercept form.
4) Use your equation to predict the number of gallons of gas bought if $12 were spent.
1) scatterplot should be increasing over time
2) positive correlation
3) equation: y= 0.3x-0.3
y-3 = 0.3(x-11)
y-3= 0.3x - 3.3
y= 0.3x -0.3
4) 12 dollars spent: y= 0.3(12) -0.3= 3.3 gallons bought.
500
Find two points that lie on a line with slope -9.
answers will vary
500
Graph x+4y=8, 4x-y=-1, x+4y=-12, and 4x-y=20 in the same coordinate plane. What figure do the four lines appear to form?
a square!
500
Write an equation of the following line in standard form.
The line contains the point (-4, -7) and has the same slope as the graph of y +3 = 5(x+4).
y+3= 5x + 20
y= 5x +17
y+7= 5 (x+4)
y+7=5x+20
y=5x+13 standard form: 5x-1y= -13
500
For what value of k are the graphs of 12y=-3x+8 and 6y=kx-5 parallel? For what value of k are they perpendicular?
parallel: y= -1/4x +2/3
y= k/6 x -5/6
k would have to equal -3/2
perpendicular:-1/4 and 4 so k/6=4 would imply k=24
500
Describe three real world scenarios:
One with a positive correlation, one with a negative correlation, and one with no correlation.
answers will vary