Point Slope Form
Write an equation that passes through (2, 0) and has a slope of - 5.
y = -5(x - 2)
*this is the same as y - 0 = -5(x - 2)
Write an equation in slope-intercept form for a line that passes through (2, -1) and has a slope of 4.
y = 4x - 9
Write an equation in slope-intercept to model the following.
There is currently 1/2" of snow on the ground. It snows 3" per week for the rest of the winter.
y = 3x + 1/2
Calculate the slope of the line through (-3, 5) and (3, -1)
-1
Each notebook in a store costs $3, and each eraser costs $2. If you want to spend exactly $18, write an equation in standard form modeling this situation.
3x + 2y = 18
A Caribbean nation produced 0.7 million tons of cane sugar. Annual production was projected to decrease by 0.05 million tons each year. Write an equation to model the situation.
y = - 0.05x + 0.7
Write the equation in slope-intercept of the line through the origin and (4, 8)
y = 2x
Museum entry is $15 per person and parking is $20 for the vehicle. Model the cost of admission, assuming everyone travels together in one vehicle.
If your cost is $80, how many people visited the museum?
y = 15x + 20
4 people visited
A tank starts with 700 gallons. Water is drained at a rate of 15 gallons per minute. Define your variables and write an equation in slope-intercept form for this situation.
y = total water in gallons
x = # of minutes
y= - 15x + 700
*pay attention to the negative!
Find the x and y intercept of the equation, 7x + 4y = 12.
x intercept: 12⁄7
y intercept: 3
Write an equation in standard form of the line that passes through (-5, 3) and has a slope of -2.
Hint: Start with writing an equation in point slope form
2x + y = -7
In a supermarket, each box of veggie burgers costs $4, and each carton of juice costs $3. If you want to spend exactly $24, what are three different combinations of groceries you could buy?
0 burgers, 8 juice cartons
3 burgers, 4 juice cartons
6 burgers, 0 juice cartons
Write an equation that passes through (2, -1) and has has the same slope (is parallel) to the equation y = 4x.
y + 1 = 4(x - 2)
Write the equation 5x - 4y = 20 in slope-intercept form.
y = 5⁄4x - 5
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Write y - 3 = 1/3(x + 6) in slope-intercept form.
y = 1/3x + 5
A new shoe shop gains 20 new shoes for its inventory each day. On the 5th day, it had 180 shoes. Write an equation in point-slope form modeling the number of shoes the shop has based on the days that has passed.
y - 180 = 20(x - 5)