Question

graphing lines & cupids arrow
name: name
love is in the air and all sorts of crazy matches are being made by cupid. cut out the equations, graph the line, and match the line to its soul - mate. you have found your soulmate when your line runs through it (just like cupids arrow). each line should only run through one soul - mate. if your line runs through more than one soul - mate, you were not precise enough.
linear equations to be graphed
cut out & paste next to the correct match

1. $y = \frac{1}{4}x + 7$
2. $y = x - 9$
3. $y = -\frac{3}{2}x$
4. $y = 6x + 11$
5. $y = -4x$
6. $y = x + 14$
7. $y = -\frac{1}{2}x - 4$
8. $y = -\frac{4}{3}x + 18$
9. $y = \frac{2}{3}x + 9$
10. $y = \frac{3}{2}x$
11. $y = -x + 2$
12. $y = \frac{1}{4}x - 13$

Explanation:

Step1: Identify slope-intercept form

All equations use $y=mx+b$, where $m$=slope, $b$=y-intercept.

Step2: Plot y-intercept first

For each equation, mark $(0, b)$ on the y-axis.

Step3: Use slope to find 2nd point

Slope $m=\frac{\text{rise}}{\text{run}}$:

• For $y=\frac{1}{4}x+7$: $b=7$, $m=\frac{1}{4}$. From $(0,7)$, move up 1, right 4. This line passes through the top-left heart character.
• For $y=x-9$: $b=-9$, $m=1$. From $(0,-9)$, move up 1, right 1. This line passes through the bottom-left rabbit character.
• For $y=-\frac{3}{2}x$: $b=0$, $m=-\frac{3}{2}$. From $(0,0)$, move down 3, right 2. This line passes through the bottom-right bear character.
• For $y=6x+11$: $b=11$, $m=6$. From $(0,11)$, move up 6, right 1. This line passes through the top-right flying character.
• For $y=-\frac{1}{4}x-7$: $b=-7$, $m=-\frac{1}{4}$. From $(0,-7)$, move down 1, right 4. This line passes through the bottom-left heart character.
• For $y=-4x$: $b=0$, $m=-4$. From $(0,0)$, move down 4, right 1. This line passes through the left-middle hat character.
• For $y=x+14$: $b=14$, $m=1$. From $(0,14)$, move up 1, right 1. This line passes through the top-middle bull character.
• For $y=-\frac{1}{2}x-4$: $b=-4$, $m=-\frac{1}{2}$. From $(0,-4)$, move down 1, right 2. This line passes through the bottom-middle girl character.
• For $y=-\frac{4}{3}x+18$: $b=18$, $m=-\frac{4}{3}$. From $(0,18)$, move down 4, right 3. This line passes through the top-middle rabbit character.
• For $y=\frac{2}{3}x+9$: $b=9$, $m=\frac{2}{3}$. From $(0,9)$, move up 2, right 3. This line passes through the right-middle mouse character.
• For $y=\frac{3}{2}x$: $b=0$, $m=\frac{3}{2}$. From $(0,0)$, move up 3, right 2. This line passes through the bottom-middle boy character.
• For $y=-x+2$: $b=2$, $m=-1$. From $(0,2)$, move down 1, right 1. This line passes through the left-middle cupid character.
• For $y=\frac{1}{4}x-13$: $b=-13$, $m=\frac{1}{4}$. From $(0,-13)$, move up 1, right 4. This line passes through the right-middle monkey character.

Answer:

1. $y=\frac{1}{4}x+7$ → Top-left heart character
2. $y=x-9$ → Bottom-left rabbit character
3. $y=-\frac{3}{2}x$ → Bottom-right bear character
4. $y=6x+11$ → Top-right flying character
5. $y=-\frac{1}{4}x-7$ → Bottom-left heart character
6. $y=-4x$ → Left-middle hat character
7. $y=x+14$ → Top-middle bull character
8. $y=-\frac{1}{2}x-4$ → Bottom-middle girl character
9. $y=-\frac{4}{3}x+18$ → Top-middle rabbit character
10. $y=\frac{2}{3}x+9$ → Right-middle mouse character
11. $y=\frac{3}{2}x$ → Bottom-middle boy character
12. $y=-x+2$ → Left-middle cupid character
13. $y=\frac{1}{4}x-13$ → Right-middle monkey character