Point-Slope Form
Write an equation for a line that goes through (1,-4) and has a slope of 3.
y+4=3(x-1)
Which of the following are written in standard form?
a. y = 3x + 2
b. 10x-15y-25=0
c. 20x-12y=33
C
A. slope-intercept form
B. constant isn't on right side of equation
What is slope-intercept form and what information does it tell us about the equation?
y = mx+b
Slope, y-intercept
What is true about the slopes of parallel lines?
They are the same
Given the equation below, what is the slope and point?
y+8=3(x-7)
slope = 3
point = (7,-8)
Find the x and y intercepts of the following equation:
x +7y=-21
(-21,0) (0,-3)
Write the equation of a line, in slope-intercept form, that has a slope of 7 and y-intercept of -8
y = 7x - 8
What is true about the slopes of perpendicular lines?
They are opposite reciprocals
Write an equation in point-slope form that is parallel to the line y=2x+4 and passes through the point (3,2)
y-2=2(x-3)
Find the x and y intercepts of the following equation
4x-9y=-20
(-5,0) (0,20/9)
Write an equation of a line that passes through (5,6) and (0,11).
y=-x+11
Write an equation in any form for a line that passes through (3,2) and is parallel to y=-4x+2
y-2=-4(x-3)
y=-4x+14
4x+y=14
Write an equation of a line in point-slope form that passes through (-4,11) and is perpendicular to a line that has a slope of 3/4.
y-11=-4/3(x+4)
You are running a concession stand at a basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you made $200. Let x represent the number of hot dogs an y represent the number of sodas sold.
Write an equation in standard form to represent this situation.
x+0.5y=200
A bike rental company allows you to rent a bike for a $4 fee plus $1.50 per hour.
1. Write an equation in slope-intercept form that models this situation.
2. What is the slope and y-intercept?
1. y = 4 + 1.5x
2. slope: 1.5; y-int: (0,4)
Write the equation of the line passing through the point (12,3) that is perpendicular to y=4/3x+5
y-3=-3/4(x-12)
y=-3/4x+12
Write an equation in point-slope form that goes through the points (4,-5) and (1,4)
y-4=-3(x-1)
or y+5=-3(x-4)
Faith was working admissions to the basketball game. The tickets are $5 for students (x) and $10 for adults (y).
1. If Faith made $500 at the game on ticket sales, write an equation in standard form that represents this scenario.
2. What are the x and y intercepts? What do they mean for this situation?
1. 5x + 10y = 500
2. (100,0) -> only student tickets were sold and there were 100 students at the game.
(0,50) -> only adult tickets were sold and there were 50 adults at the game.
An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute.
1. Write an equation in slope-intercept form to model this situation.
2. Find the altitude of the plane after 5 minutes.
1. y = 30,000-2000x
2. 20,000 feet
1. Write the equation of the line passing through the point (-1,3) that is perpendicular to y=-2x+6
2. Write the equation of the line passing through the point (-1,3) that is parallel to y=-2x+6
1.
y-3=1/2(x+1)
1. y-3=-2(x+1)