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We can manipulate simple equations:
1. Finding Δy given Δx and m We can manipulate simple equations: 12 = x 8 12 = 8x
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We can also manipulate the slope formula: 1.
Finding Δy given Δx and m Remember: = (y2 – y1) = (x2 – x1) ΔY ΔX NOTE: We are solving for ΔY, NOT the value of Y ΔY means Change in Y ΔY = m ΔX ΔY = m ΔX
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What is ΔY given ΔX is 4 and m is 8?
1. Finding Δy given Δx and m Example: What is ΔY given ΔX is 4 and m is 8? ΔY = m ΔX m 8 ΔX 4 ΔY = 8 4 ΔY ? 32 ΔY = 32
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1. Example: = = = = m m 45 mph ΔY m ΔX ΔX 3.5 hrs ΔY 45 3.5 ΔY ?
Finding Δy given Δx and m Example: How many miles do you travel (Δ Distance) given you travel 3.5 hours (Δ Time) and you are driving at 45mph? ΔDistance = m Δ Time m 45 mph ΔY = m ΔX ΔX 3.5 hrs ΔY = 45 3.5 ΔY ? 157.5 mi ΔY = 157.5 mi
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NOTE: We are solving for ΔX, NOT the value of X
2. Finding Δx given Δy and m 2. We can also manipulate the slope formula: ΔY = m ΔX NOTE: We are solving for ΔX, NOT the value of X ΔY = ΔX m
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What is ΔX given ΔY is 38 and m is 4?
2. Finding Δx given Δy and m 2. Example: What is ΔX given ΔY is 38 and m is 4? ΔY = ΔX m m 4 ΔX ? 9.5 38 = ΔX ΔY 38 4 9.5 = ΔX
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Example: 2. 2. = = = = m ΔY m 50 mph ΔX m ΔX ? 1.6 hrs 80 ΔX ΔY
How many hours do you travel (Δ Time) given you drive for 80 miles (Δ Distance) and you are traveling at 50mph? 2. Finding Δx given Δy and m 2. ΔDist. = Δ Time m ΔY m 50 mph = ΔX m ΔX ? 1.6 hrs 80 = ΔX ΔY 80 miles 50 1.6 hrs = ΔX
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(y2 – y1) = (x2 – x1) = 3. = = = ΔY ΔX ΔY m ΔX ΔY m ΔX ΔY ΔX m
Review of Delta and Slope Formulas ΔY = m ΔX ΔY = m ΔX ΔY = ΔX m
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