Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
match each pair of points to the equation of the line that is parallel to the line passing through the points.

b(5, 2) and c(7, -5)
d(11, 6) and e(5, 9)
y = -0.5x - 3
y = -3.5x - 15
f(-7, 12) and g(3, -8)
y = 5x + 19
h(4, 4) and i(8, 9)
y = 1.25x + 4
j(7, 2) and k(-9, 8)
l(5, -7) and m(4, -12)

Explanation:

Step1: Find slope of B(5,2) and C(7,-5)

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-5 - 2}{7 - 5} = \frac{-7}{2} = -3.5$
Equation with slope -3.5: $y = -3.5x - 15$ (matches slope)

Step2: Find slope of D(11,6) and E(5,9)

$m = \frac{9 - 6}{5 - 11} = \frac{3}{-6} = -0.5$
Equation with slope -0.5: $y = -0.5x - 3$ (matches slope)

Step3: Find slope of F(-7,12) and G(3,-8)

$m = \frac{-8 - 12}{3 - (-7)} = \frac{-20}{10} = -2$? Wait, no—wait, $y = 5x + 19$? Wait, no, recalculate:
Wait, $m = \frac{-8 - 12}{3 - (-7)} = \frac{-20}{10} = -2$? No, wait, $y = 5x + 19$ has slope 5. Wait, maybe I messed up. Wait, J(7,2) and K(-9,8):
$m = \frac{8 - 2}{-9 - 7} = \frac{6}{-16} = -0.375$? No, wait, F(-7,12) and G(3,-8):
Wait, $y = 5x + 19$ slope 5. Let's check H(4,4) and I(8,9):
$m = \frac{9 - 4}{8 - 4} = \frac{5}{4} = 1.25$
Equation with slope 1.25: $y = 1.25x + 4$ (matches)

Step4: Find slope of L(5,-7) and M(4,-12)

$m = \frac{-12 - (-7)}{4 - 5} = \frac{-5}{-1} = 5$
Equation with slope 5: $y = 5x + 19$ (matches)

Step5: J(7,2) and K(-9,8)

Wait, earlier mistake: J(7,2) and K(-9,8):
$m = \frac{8 - 2}{-9 - 7} = \frac{6}{-16} = -0.375$? No, wait, F(-7,12) and G(3,-8) slope:
Wait, F(-7,12) and G(3,-8): $m = \frac{-8 - 12}{3 - (-7)} = \frac{-20}{10} = -2$? No, this is confusing. Wait, let's re-express:

Correct matches:
- B(5,2) & C(7,-5) ↔ $y = -3.5x - 15$ (slope -3.5)
- D(11,6) & E(5,9) ↔ $y = -0.5x - 3$ (slope -0.5)
- H(4,4) & I(8,9) ↔ $y = 1.25x + 4$ (slope 1.25)
- L(5,-7) & M(4,-12) ↔ $y = 5x + 19$ (slope 5, since $m = \frac{-12 - (-7)}{4 - 5} = 5$)
- F(-7,12) & G(3,-8): Wait, $m = \frac{-8 - 12}{3 - (-7)} = -2$, but no equation with slope -2. Wait, maybe J(7,2) and K(-9,8):
$m = \frac{8 - 2}{-9 - 7} = \frac{6}{-16} = -0.375$? No, this is wrong. Wait, original tiles:

Wait, correct slopes:
- B(5,2)-C(7,-5): slope -3.5 → $y = -3.5x - 15$
- D(11,6)-E(5,9): slope -0.5 → $y = -0.5x - 3$
- H(4,4)-I(8,9): slope 1.25 → $y = 1.25x + 4$
- L(5,-7)-M(4,-12): slope 5 → $y = 5x + 19$
- F(-7,12)-G(3,-8): slope -2? No, wait, $y = 5x + 19$ slope 5, L(5,-7)-M(4,-12) slope 5 (correct).
- J(7,2)-K(-9,8): slope $\frac{8-2}{-9-7} = \frac{6}{-16} = -0.375$? No, maybe I made a mistake. Wait, F(-7,12) and G(3,-8):
Wait, $y = 5x + 19$ slope 5. L(5,-7) and M(4,-12): $m = \frac{-12 - (-7)}{4 - 5} = \frac{-5}{-1} = 5$ (correct). So L&M ↔ $y = 5x + 19$

F(-7,12) and G(3,-8): $m = \frac{-8 - 12}{3 - (-7)} = -2$, but no equation. Wait, maybe J(7,2) and K(-9,8):
$m = \frac{8 - 2}{-9 - 7} = \frac{6}{-16} = -0.375$? No, this is error. Wait, original problem: tiles are B, C; D, E; F, G; H, I; L, M; and equations: $y=-3.5x-15$, $y=-0.5x-3$, $y=5x+19$, $y=1.25x+4$.

So correct pairs:
1. B(5,2) and C(7,-5) ↔ $y = -3.5x - 15$ (slope -3.5)
2. D(11,6) and E(5,9) ↔ $y = -0.5x - 3$ (slope -0.5)
3. H(4,4) and I(8,9) ↔ $y = 1.25x + 4$ (slope 1.25)
4. L(5,-7) and M(4,-12) ↔ $y = 5x + 19$ (slope 5)
5. F(-7,12) and G(3,-8): Wait, no equation? Wait, maybe J(7,2) and K(-9,8):
Wait, J(7,2) and K(-9,8): $m = \frac{8 - 2}{-9 - 7} = \frac{6}{-16} = -0.375$? No, this is wrong. Wait, maybe I miscalculated F(-7,12) and G(3,-8):
Wait, $y = 5x + 19$ slope 5. L(5,-7) and M(4,-12): $m = 5$ (correct). H(4,4) and I(8,9): $m = 1.25$ (correct). B and C: $m = -3.5$ (correct). D and E: $m = -0.5$ (correct). Then F(-7,12) and G(3,-8): $m = \frac{-8 - 12}{3 - (-7)} = -2$, but no equation. Wait, maybe J(7,2) and K(-9,8) is a typo? No, the problem says "not all tiles will be used". So the four pairs are:

- B(5,2) & C(7,-5) ↔ $y = -3.5x - 15$
- D(11,6) & E(5,9) ↔ $y = -0.5x - 3$
- H(4,4) & I(8,9) ↔ $y = 1.25x + 4$
- L(5,-7) & M(4,-12) ↔ $y = 5x + 19$

Answer:

• B(5, 2) and C(7, -5) ↔ \( y = -3.5x - 15 \)
• D(11, 6) and E(5, 9) ↔ \( y = -0.5x - 3 \)
• H(4, 4) and I(8, 9) ↔ \( y = 1.25x + 4 \)
• L(5, -7) and M(4, -12) ↔ \( y = 5x + 19 \)

(Note: F(-7, 12) and G(3, -8) and J(7, 2) and K(-9, 8) have no matching equation in the tiles provided, as their slopes don’t match the given equations.)