Coordinate Plane
Name the quadrant that contains the point (−3,5)(−3,5).
Quadrant II
Define slope in words.
Slope = change in y over change in x (rise/run)
Write the slope‑intercept form of a line and explain what each letter represents.
y=mx+by=mx+b where m is the slope and b is the y‑intercept
Find the slope of the line through (0,1)(0,1) and (2,5)(2,5).
m=2
T-Mobile offers a data plan that charges a base fee of $15 per month and $5 for each gigabyte of data used. Write an equation in slope-intercept form to represent the total monthly cost based on the gigabytes of data used.
y=5x+15
Plot the point (4,−2)(4,−2) and state whether it is left/right of the y‑axis and above/below the x‑axis.
Point (4,−2)(4,−2) is right of the y‑axis and below the x‑axis.
Determine whether the line through (1,2)(1,2) and (1,−4)(1,−4) is horizontal, vertical, or neither.
Vertical line
For the equation y=3x+2y=3x+2, identify the slope and the y‑intercept.
Slope 3, y‑intercept (0,2) or b=2
Given the table: x: 1, 2, 3; y: 4, 7, 10. What is the slope of the line modeled by this table?
m=3
During a vacation at the beach, Sarah decides to rent a bike. The rental shop charges a flat fee of $10 plus $3 per hour of use. Write a slope-intercept equation to represent the total cost y of renting the bike for h hours.
y=3h+10
What are the coordinates of the point that is 3 units right of the origin and 4 units up from the origin? Write as (x,y).
(3,4)
Explain what a slope of 0 means about a line's direction.
Slope of 0 means the line is horizontal (no vertical change).
Graph the line y=−12x+4y=−21x+4 by listing two points you could plot.
Two possible points: when x=0, y=4 → (0,4); when x=2, y=3 → (2,3) (since y=−1/2(2)+4=3)
A line passes through (−2,−1) and (2,7). Find the slope.
m=2
A taxi charges a base fee of $3 plus $2.50 per mile. Let y be the total fare and x the miles driven. Write an equation in slope‑intercept form and identify slope and y‑intercept.
y=2.5x+3.
Slope (rate per mile) 2.5
y‑intercept (base fee) 3.
A point lies on the x‑axis and is 7 units to the left of the origin. Give its coordinates.
(−7,0)
A line rises 5 units when moving 2 units to the right. What is its slope? Express as a fraction.
Slope 5/2
Convert the equation 2y−6=4x2y−6=4x into slope‑intercept form y=mx+by=mx+b.
2y−6=4x → 2y=4x+6 → y=2x+3
Find the slope of the line given by the standard form equation 3x+4y=12 by converting to slope‑intercept form first.
m= -3/4
An elf is delivering gifts along a straight street. He starts at the toy factory, which is located 3 miles from the beginning of the street. The elf delivers gifts at a rate of 2 gifts per mile. Write the slope-intercept equation for this situation.
y=2x+3
A delivery drone is tasked with dropping gifts at specific locations. It starts at point (2, 5) and needs to drop a present at point (7, 5). How many units does the drone need to move horizontally to reach the drop-off point?
5
Describe what an undefined slope means and give an example pair of distinct points that produce an undefined slope.
Undefined slope means vertical line; example points: (2,1) and (2,5).
A line has slope 2/3 and passes through the point (3,5). Write its equation in slope‑intercept form.
y=2/3x+3.
Alex is shopping for cereal at the grocery store. He notices that the more boxes he buys, the more discount he receives. Here is the table he created:
Number of Boxes Total Cost
2 $5
4 $9
6 $13
Determine the slope of the total cost with respect to the number of boxes.
m=$2
In Fortnite, a new area is being designed with a sloped hill. The hill starts at a height of 20 meters on the map at point (2, 20) and reaches a height of 50 meters at point (8, 50). Write the equation of the line representing the hill's slope in slope-intercept form. (Hint: Find the slope first. Then make a table to find the y-intercept; x will be 0.)
y=5x+10