Lines Each & Elves Lines To Be Graphed: Y = 15x + 7 Y = -2x – 17 Y = -14x – 15 Y = 12x – 3 Y = 125x Y = 83x – 8 Y = (5/4)x – 4 Y = -4x + 15 Y = -2x – 8 Y = x + 8 Y = -xtll Y = 716x + 4 – 8×47 J – ax – 3 Y – 8x 4 – 5x + 7 Y – #X – 15
The Correct Answer and Explanation is:
To solve the “Graphing Lines & Catching Elves” activity, we need to match each linear equation from the list on the left with the elves shown on the graph, based on the lines they are sitting or standing on. The matching is done by plotting the lines from the equations and identifying which elf lies on each line.
Equations and Matching Elves:
Let’s match the elves to their equations from the graph and answer key shown at the bottom of the image.
From the image, the bottom section shows elves already matched with their equations. We’ll verify and explain a few key examples:
- y = -2x – 17 → Elf near the bottom left (shown holding a wrench).
- y = 5/4x – 4 → Elf in the middle left (near a candy cane).
- y = -4x + 15 → Elf near bottom center (on a sled).
- y = 1/5x + 7 → Elf near top right (on a skateboard).
- y = 12/5x → Elf center-right (flying in air).
- y = 1/2x – 3 → Elf middle right (ice skating).
- y = 8/3x – 8 → Elf lower middle-right.
- y = -x + 11 → Elf at upper middle-left.
- y = x + 8 → Elf on top left (in a jetpack).
- y = 7/6x + 1 → Elf mid-lower right.
- y = -1/4x – 15 → Elf bottom middle (next to sled elf).
- y = -2x – 8 → Elf on lower left-middle.
Explanation
This activity combines graphing linear equations with a visual puzzle, making it an engaging way to practice slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To solve it, we observe where each elf sits on the grid. Each elf lies exactly on a straight line, and our goal is to determine which equation’s line passes through that position. The equations differ in slope and intercept. By understanding how these values affect the graph (slope determines the tilt of the line; intercept determines where it crosses the y-axis), we can estimate or calculate the correct placement.
Matching elves involves either visually plotting the line by identifying the slope and intercept or checking if specific coordinates on the graph satisfy a given equation. The answer section below the grid shows correctly matched equations with elf images, offering confirmation.
This kind of activity enhances students’ spatial reasoning and reinforces key algebraic concepts, particularly the graphical interpretation of equations. It is a clever and visual way to learn how linear equations behave and intersect on the coordinate plane.
