Slope
What is the slope of a horizontal line?
0
What is the slope-intercept form for when the temperature at sunset is 66°F and decreases by 3° per hour?
y = -3x + 66
What is the formula for point-slope form?
y - y1 = m(x - x1)
What is the equation for standard form?
Ax + By = C
Suppose that a bike rents for $4 plus $1.50 per hour. Write the equations in slope-intercept form. How much would it cost to rent it for 8 hours?
y=1.50x+4
$16
What is the slope of a vertical line?
Undefined
Write the following in slope-intercept form 2x – 3y = 6
y= 2/3x -2
Write the point-slope form for the following: (-4, 5) with slope -1/3
y - 5 = -1/3(x + 4)
Given 3x - 2y = 12, what are the intercepts?
x = 4 (4,0)
y = -6 (0,-6)
A 100-point test has x questions worth 2 points each and y questions worth 4 points each. If there were 19 4-point questions, how many 2-point questions were there? Write the equation in standard form and solve.
2x+4y=100
12 2-point questions
What do we know about the slope of parallel lines?
The slopes are equal.
Write the following in slope-intercept form: A line that goes through (-2, 5) and has a slope of -4.
y = -4x -3
Identify the point and slope for the following: y + 5 = -3(x - 4)
Point: (4, -5) Slope: -3
Convert the slope intercept form to standard form: y = 2x + 5
2x - y = -5
or
-2x + y = 5
Faith was working admissions to the basketball game. The cost was $5 for students (x) and $7 for adults (y). If they made $500 dollars at the game on ticket sales, write an equation in standard form that represents this scenario. If they sold 40 adult tickets, how many student ticket did they sell?
5x+7y=500
44 student tickets
Find the slope (-4, -5) (6, 12)
17/10
Write the following in slope-intercept form: (-6, 1) and (4, -4).
y = -1/2x -2
Write the following in point-slope form:
(3, 4) and (-2, -5)
y - 4 = 9/5(x - 3) OR
y + 5 = 9/5(x + 2)
Write the equation of a line that goes through (3, −1) with a slope of −1 in standard form
x + y = 2
For four months, you have saved $25 per month. You now have $175 in your savings account. What equation represent this in point-slope form? How much money did the account start with?
y-175=25(x-4)
The account started with $75
It takes Shelly 20 minutes to deliver 10 newspapers and 60 minutes to deliver 40 newspapers. Find the rate of change. Round to the nearest hundredth.
0.75 papers per minute
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation.
y=4x+30
Mary is ascending in a hot air balloon at an average speed of 2 meters per second. After 30 seconds the balloon is at 60 meters. Write an equation in point-slope form to find the altitude y (in meters) for any number of seconds x.
y - 60 = 2(x - 30)
In a store, you sell long-sleeve shirts for $10 and short-sleeve shirts for $8. Write an equation in standard form that represents the number of long-sleeve and short-sleeve shirts you must sell to earn $400.
10x + 8y = 400
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is a point-slope equation for the climber? What would be his altitude after 8 hours?
y-400=75(x-2) or y-700=75(x-6)
His altitude would be 850 feet.