Slope
Solve for the slope passing through the points: (2, 5) and (6, 13)
m =y2-y1 / x2-x1
13 - 5 / 6 - 2
= 8 / 4
= 2
What is the y intercept of the equation?
y = x - 8
y-intercept: -8
Sarah is selling lemonade. She pays $10 for a stand and makes $3 for every cup she sells. Write the equation for her total earnings y after selling x cups. What is the slope? What is the y-intercept?
Equation: y = 3x - 10
Slope: 3 (earnings per cup), Y-intercept: 10 (cost of stand)
The slope-intercept form of a linear equation is ____________.
y = mx + b
Write the equation of the line in slope-intercept form:
A line has a slope of 2 and a y-intercept of -5.
y = 2x - 5
Solve for the slope passing through the points: (5, 1) and (9, -3)
m =y2-y1 / x2-x1
=-3 - 1 / 9 - 5
= -4 / 4
= -1
What is the y intercept for :
y = 0.75x
y-intercept: 0
A gym membership costs $30 to sign up and $10 per month. Write the equation for the total cost y after x months. What is the total cost after 6 months?
Equation: y = 10x + 30
After 6 months: y = 10 * 6 + 30 = 60 + 30 = 90
Total cost: $90
The line passes through the y-axis at 6 with a slope of 1.
y = 1x + 6 or y = x + 6
If the slope is positive, the line goes __ as you move from left to right.
upward
For the equation below, write the slope.
y = -2
Slope: 0
What is the y-intercept of the equation:
y = -4
y-intercept: -4
A babysitter already has $25 saved and earns $8 per hour. Write the equation for total money y after x hours of babysitting. How much money will the babysitter have after 5 hours?
Equation: y = 8x + 25
For x = 5: y = 8 * 5 + 25 = 40 + 25 = 65
Total money: $65
The letter b in y = mx + b shows where the line crosses the __.
y-intercept or y-axis
A parking garage charges $5 per hour, with no entrance fee. Write the equation for the total cost y for x hours. What do the slope and y-intercept mean?
Equation: y = 5x
Slope: 5 (per hour), Y-intercept: 0 (no entrance fee)
A concert ticket costs $12 each, and there are no additional fees. What is the slope?
Slope: 12
Identify the y-intercept in the equation:
y = x - 9
y intercept is -9
A taxi charges a base fare of $4 and $1.50 per mile. Write an equation for the total fare y for x miles. What do the slope and y-intercept represent?
Equation: y = 1.5x + 4
Slope: 1.5 (cost per mile), Y-intercept: 4 (base fare)
The line passes through the y-axis at 7 and has a slope of 2.
y = 2x + 7
Match each description to the correct equation.
A line with no y-intercept (passes through the origin) and a slope of 2.
y = 2x
A water tank is filled with 50 liters of water and 15 more liters are added every hour. What is the slope?
Slope: 15
Where can you find the y-intercept?
It can be found where the line crosses the y axis.
The day you were born, your grandmother put $500 in an account to help you pay your college expenses. Every year, on your birthday, she adds $50 to the account. What is the equation to represent this. How much money will be in the account when you are 14 years old?
Equation: y = 50x + 500
For x = 14: y = 50 *14 + 500 = 700 + 500 = 1200
Total money: $1200
The temperature at sunrise is 40 degrees. It rises by 3 degrees every hour. Write an equation for the temperature y after x hours. What does the slope mean? What does the y-intercept represent?
Equation: y = 3x + 40, slope means the temperature rises 3 degrees per hour, y-intercept is the temperature at sunrise (40 degrees)
A babysitter already has $16 and earns $7 per hour. What is the equation for the total dollars in the slope intercept form?
If the babysitter has $58, how many hours did they work?
y = 7x + 16
58 = 7x + 16
42 = 7x
x = 6 hours